# Workshop

#### Dates: 21st to 25th, August

The Workshop aims to convene some of the world’s experts in quantum information to discuss the latest results in this and related fields. The main aim is to provide a relaxed setting, avoiding an excess of talks, in order to stimulate discussion and new ideas.

#### Workshop Schedule

Monday (21/08) Tuesday (22/08) Wednesday (23/08) Thursday (24/08) Friday (25/08)
08:30-08:55 Opening
09:00-09:25 G. Lemos J. Monsel F. Brandão D. Gerace J. Bermejo-Vega
09:30-09:55 A. Khoury C. Cormick S. Boettcher E. Bäumer C. Napoli
10:00-10:25 W. Vogel F. Nicácio M. Richard P. Erker E. Agudelo
10:30-10:55 Coffee-break Coffee-break Coffee-break Coffee-break Coffee-break
11:00-11:25 P-L de Assis D. Felinto K. Modi R. Nichols R. Serra
11:30-11:55 E. Denning P. Saldanha S. Pádua F. Toscano A. Auffeves
12:00-12:25 F. Tacchino G. Landi R. de Araújo G. Aguilar Closing
12:30-16:00 Lunch Lunch Lunch Photo (15 min)
boat trip
16:00-16:25 G. Lima A. Sawicki M. Araújo boat trip
16:30-16:55 J. Bohr M. Oszmaniec F. Parísio boat trip
17:00-17:25 D. Cavalcanti D. Brod Y. Guryanova boat trip
17:30-17:55 Coffee-break Coffee-break boat trip
18:00-18:25 J. Pienaar R. Drumond boat trip
18:30-18:55 R. Chaves L. Aolita
19:00-21:30 poster session

### Titles and abstracts

•  Gabriela B. Lemos. Indistinguishability, coherence and interference visibilities.
I will introduce the phenomenon of induced coherence without induced emission, for those unfamiliar with the topic. I’ll then talk about how correlations and entanglement in photon pairs can be quantified by detecting only one photon in each pair, using only lowest order interference visibility measurements.
• Antônio Z. Khoury. Quantum information concepts in classical optics.
Entanglement is an essential resource for quantum information protocols. Generating, controlling and characterizing it are necessary tasks for realistic implementations of quantum information schemes. Despite its fundamental role in the realm of quantum theory, entanglement has also found important analogies in classical optics. We discuss non separable polarization-transverse mode structures and their characterization through inequality criteria analogous to those used in quantum theory to rule out local hidden variable models. Vector beams are well known realizations of such non separable structures that can be evidenced through an inequality criterion analogous to Bell’s inequality in Quantum Mechanics. Many quantum information protocols can be mimicked in the classical domain using this formal analogy, allowing simple optical platforms to test mathematical properties of entanglement. Moreover, this notion can be extended to three degrees of freedom to investigate the tripartite non separability of transverse, longitudinal and polarization parts of a laser beam. Quantum information analogies in Classical Optics open new perspectives in coherence theory inspired by quantum protocols. One example is the spin to orbital mode transfer through a classical optical analog of quantum teleportation.
• Werner Vogel. Efficient Techniques to Verify Quantum Phenomena of Light
Novel measurement strategies are considered, which render it possible to efficiently verify quantum correlations of radiation fields. We have implemented a direct sampling technique for nonclassicality quasiprobabilities which visualizes quantum effects via negativities. Compared with standard balanced homodyning, the quadrature phase is continuously measured to avoid systematic errors. We also proposed the method of unbalanced homodyne correlation measurements to access normal-ordered moments of the displaced photon number operator. To verify multipartite entanglement, we developed optimal entanglement witnesses for Gaussian quantum states. We also show that in the absence of so-called genuine multipartite entanglement highly efficient multipartite entanglement may exist. Finally, we consider general space-time dependent quantum correlations of light. As an example, we experimentally demonstrate anomalous quantum correlations of squeezed light, which show quantumness beyond the limited phase range of squeezing. A dephased two-mode squeezed vacuum state is of interest as it shows quantum correlations beyond entanglement and discord. Such correlations have been verified by the joint measurement of the click counting statistics of a time-multiplexing setup.
• Pierre-Louis de Assis. A method for mapping the position of quantum emitters using stress gradients
Semiconductor quantum dots (QDs) are one of the most used solid state single photon sources, being used as two- or even three-level artificial atoms. InAs QDs are nanocrystals grown on top of a GaAs substrate. Due to the nature of the QD fabrication, their position on the substrate, as well as their individual emission energy, are randomly distributed. This makes their use in quantum applications a challenge.
As we have previously demonstrated, the mode of a mechanical oscillator can be very efficiently coupled to the emission energy of QDs embedded in it, via stress applied on them by structural deformation during oscillation. This strong response to stress, along with a stress profile that has a very large gradient, allows us to associate the energy shift of photons emitted while the mechanical mode is resonantly excited to the position of the QD they originated from.
We present a procedure to map the position of QDs by monitoring the change in their photoluminescence spectra when submitted to stress gradients, and demonstrate it using In(Ga)As QDs deeply embedded in a tapered GaAs waveguide. The waveguide constituted a mechanical oscillator that had its first flexural mode split in two, oscillating along orthogonal directions. The large stress fields generated in this structure allowed us to map the position of the QDs with an accuracy between 35 and 1 nm, comparable to techniques that use near-field imaging and require QDs to be very close to the surface of the sample.
• Emil Vosmar Denning. Robust multi-photon entanglement protocol using a charged quantum dot
Spin-photon and multi-photon entanglement are crucial for the realisation of optical quantum computers and quantum communication devices. Charged quantum dots (QDs) constitute a promising platform due to their internal spin degree of freedom that can mediate photon-photon entanglement. The main limitation to this platform is posed by the nuclear spin environment in the semiconductor host material of the QD. The nuclear spins act as an effective magnetic Overhauser field that fuctuates on a microsecond time scale, deteriorating the entanglement coherence.To alleviate this problem, we propose a spin-mediated multi-photon entanglement protocol that works by scattering single photons on a charged QD in a constant external magnetic field in the Voigt configuration. The robustness of the protocol is attributed to two particular features. First, energy conservation in the photon-QD scattering process protects the coherence of the entangled state against nuclear spin-induced ensemble dephasing for any number of photons. This ensures scalability to multi-photon entangled states which would not be possible by extending previously demonstrated single spin-photon protocols to multiple photons. Second, we show that the external field increases the fidelity by retaining the QD eigenstructure during light-matter interaction. This is a major improvement compared to previously suggested entanglement schemes that operate without an screening external field, which we demonstrate through detailed cavity quantum electrodynamics calculations.
• Francesco Tacchino. An open quantum systems theory of the Q-cycle mechanism in cellular membranes
We present a quantum and stochastic model of the Q-cycle, the process at the heart of the photosynthetic electron transport chain and, with very small differences, of the mitochondrial respiratory chain. The work starts from a model proposed in Smirnov, Nori (2012) Phys. Biol. 9, and follows the great interest that, in recent years, arose about the application of the concepts of quantum physics to microscopic biology. The Q-cycle shows many interesting features, including efficient energetic coupling between electron transfer and proton pumping, spontaneous minimization of dissipative short-circuit events and a curious interplay between the quantum electron and proton dynamics and the stochastic motion of a moving molecule (called shuttle) that actively transports the charged particles inside the membrane. It also provides an interesting example of a mesoscopic system that can handle single excitations on a microseconds timescale. We reformulate and clarify the original model using well established theoretical methods from the physics of open quantum systems and statistical mechanics: electron binding sites are treated as individual two-level systems while the proton and electron reservoirs are described by thermal fermionic baths. In particular, electron reservoirs play the role of source and drain leads for the transport network. The master equation in Lindblad form is used to simulate the quantum mechanical part of the evolution, which is solved together with a stochastic differential equation for the mechanical motion of the shuttle. Tunnelling interaction between electron binding sites coupled to a vibrational environment in a Spin-Boson fashion is responsible for incoherent transfer with a temperature- and transition energy-dependent rate known in chemical physics as Marcus rate. We confirm the predicted efficiency and we explore the behaviour of the systems while varying external parameters such as temperature and chemical potentials of the reservoirs, obtaining clear indications about its optimality for realistic living conditions. The model and methods might be extended and applied to a variety of mechanisms of biological interest.
• Gustavo Lima. Device-independent certification of a nonprojective qubit measurement
Quantum measurements on a two-level system can have more than two independent outcomes, and in this case, the measurement cannot be projective. Measurements of this general type are essential to an operational approach to quantum theory, but so far, the nonprojective character of a measurement could only be verified experimentally by already assuming a specific quantum model of parts of the experimental setup. Here, we overcome this restriction by using a device-independent approach. In an experiment on pairs of polarization-entangled photonic qubits we violate by more than 8 standard deviations a Bell-like correlation inequality which is valid for all sets of two-outcome measurements in any dimension. We combine this with a device-independent verification that the system is best described by two
qubits, which therefore constitutes the first device-independent certification of a nonprojective quantum measurement.
• Jonatan Bohr Brask. Semi-device-independent quantum random number generation based on unambiguous state discrimination
The generation of random numbers is of paramount importance in modern science and technology, e.g. for Monte Carlo simulation, statistical sampling, cryptography, and gaming applications. Here, we develop a new approach to quantum random number generation based on unambiguous quantum state discrimination. We consider a prepare-and-measure protocol, where two non-orthogonal quantum states can be prepared, and a measurement device aims at unambiguously discriminating between them. Because the states are non-orthogonal, this necessarily leads to a minimal rate of inconclusive events whose occurrence must be genuinely random and which provide the randomness source that we exploit. Our protocol is semi-device-independent in the sense that the output entropy can be lower bounded based on experimental data and few general assumptions about the setup alone. It is also practically relevant, which we demonstrate by realising a simple optical implementation achieving rates of 16.5 Mbits/s. Combining ease of implementation, high rate, and real-time entropy estimation, our protocol represents a promising approach intermediate between fully device-independent protocols and commercial QRNGs.
• Daniel Cavalcanti. Efficient device-independent entanglement detection for multipartite systems
Detecting entanglement in systems with many particles remains experimentally and theoretically challenging. The first barrier is the exponential amount of information required to reconstruct the system’s state. The second is that, even if the quantum state is known, the available methods are computationally too demanding even for systems composed of few particles. We introduce a technique for entanglement detection that is both computationally and experimentally efficient. It involves a number of experimental configurations that grow only polynomially with the size of the system, which makes it applicable to states of up to a few tens of particles. Moreover, it is based on the knowledge of few-body correlators, making it amenable to practical implementation. Lastly, our method is device independent, meaning that it allows one to assess entanglement without assuming any prior knowledge of the prepared state or the measurements performed.
• Jacques Pienaar. A QBist approach to quantum inference
Bayesian inference is the formal process of updating probability distributions in light of new information about the variables. It is currently an open problem how to perform inference when the probabilities describe the outcomes of measurements on quantum systems. I will explain what the problems are, and how some of them can be circumvented using an approach inspired by Quantum Bayesianism (QBism).
• Rafael Chaves. Generalization of Bell’s theorem for temporal causal structures
As shown by Bell’s theorem, there is a mismatch between the classical and quantum predictions for the possible correlations between space-like separated events. In this talk we will discuss, both theoretically and experimentally, the extension of Bell’s theorem to the temporal case, that is, where events are time-like separated according to a well defined causal structure. This scenario allows for the emergence of a new kind of non-classicality, arguably simpler than Bell’s nonlocality and that have strong implications for results of fundamental importance in the field of causal inference.
• Juliette Monsel. Measuring the arrow of time in a hybrid opto-mechanical system
Irreversibility is a fundamental concept of thermodynamics, associated with the existence of time arrow for thermodynamic transformations. The degree of irreversibility of a transformation is quantified by entropy production, which can be defined at the level of single realizations. The fluctuations of such entropy production verify the celebrated fluctuation theorems, e.g. Jarzynski’s equality [1, 2]. To measure entropy production, the usual strategy is to monitor the trajectory of the small system under study. If it gave rise to successful experimental demonstrations in the classical regime [3, 4], this strategy can become problematic in the quantum regime, because of measurement back-action.

To probe fluctuation theorems, we propose another strategy based on the direct measurement of work fluctuations. More precisely, we shall exploit a hybrid optomechanical system, i.e. a two-level system (TLS) coupled to a mechanical oscillator on the one hand, and to optical photons on the other hand. It was shown in [5] that the mechanical oscillator plays the role of a battery, exchanging work with the TLS. Work exchanges can be measured, by measuring the mechanical energy at the beginning and at the end of the transformation. Here we go beyond these first results and show that mechanical fluctuations can be related to work fluctuations, providing a direct way to measure fluctuation theorems. We finally evidence that Jarzynski’s and Crooks equalities [1, 2] can be probed in state of the art devices.

References
[1] C. Jarzynski, “Nonequilibrium equality for free energy differences,” Physical Review Letters, vol. 78, no. 14, p. 2690, 1997.
[2] G. E. Crooks, “Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences,” Physical Review E, vol. 60, no. 3, p. 2721, 1999.
[3] O.-P. Saira, Y. Yoon, T. Tanttu, M. Möttönen, D. Averin, and J. P. Pekola, “Test of the jarzynski and crooks fluctuation relations in an electronic system,” Physical review letters, vol. 109, no. 18, p. 180601, 2012.
[4] F. Douarche, S. Ciliberto, A. Petrosyan, and I. Rabbiosi, “An experimental test of the jarzynski equality in a mechanical experiment,” EPL (Europhysics Letters), vol. 70, no. 5, p. 593, 2005.
[5] C. Elouard, M. Richard, and A. Auffèves, “Reversible work extraction in a hybrid opto-mechanical system,” New Journal of Physics, vol. 17, p. 055018, 2015.

• Cecilia Cormick. Simulating spin-boson models with trapped ions
We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. We illustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian.
• Fernando Nicacio (Boiúna). Determining stationary-state quantum properties directly from system-environment interactions
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering processes.
• Daniel Felinto. New types of quantum memory in cold atomic ensembles
In recent years, our group reported a series of advances in new processes to store optical information in atomic ensembles. Two main categories will be explored here. First, we described the implementation of nonlinear optical memories capable of both storing and manipulating the input information. We applied these memories to store the orbital angular momentum state of a light field, extracting in the process a field with a multiple of the input-state topological charge. Second, we store information in the external degrees of freedom of the atoms and demonstrate that such memories can be non-volatile, i.e., they can be largely insensitive to the reading process, preserving the information after it is read. In the end, we will discuss our perspectives to employ such memories to store quantum states of light.
• Pablo Saldanha. Fock-State Superradiance in a Quantum Memory
We present a theoretical and experimental study of the mechanism of extraction of information stored in a quantum memory. In our experiments, the memory may contain one or two excitations of a collective atomic state, which are mapped into a Fock state of light with one or two photons during the reading process. A theory is developed for the wavepacket of the extracted photons, leading to simple analytical expressions depending on the key parameters of the problem, like the intensity of the read field and the number of atoms in the atomic ensemble. The coherent distribution of the excitations among the atoms leads to an increase of the photons emission rates, in a phenomenon called superradiance. Our theory is compared to a large set of experimental situations and a satisfactory quantitative agreement is obtained. We were able to make a detailed study of the single-photon superradiance in the system, showing that the photon emission rate increases linearly with the number of atoms of the quantum memory. We also verified that when two photons are emitted from the memory, the emission rate of the first photon is twice the one of the second photon.
• Gabriel Teixeira Landi. The Wigner entropy production rate
The characterization of irreversibility in general quantum processes is an open problem in the field of quantum thermodynamics. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by equilibrium environments, a situation that often does not match the reality of experiments at the microscopic and mesoscopic scale. We propose a theory of irreversible entropy production that is suited for quantum systems exposed to general, non-equilibrium reservoirs. We do so by focusing on the phase space dynamics of the system and the corresponding measure of disorder, the Wigner entropy. We show that it is possible to relate the Wigner entropy production rate to irreversible probability currents in phase space, thus providing a microscopic interpretation for the irreversible component of open system dynamics.
• Adam Sawicki. Criteria for universality of quantum gates
In this talk I will consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\ldots,U_n\}\subset SU(d)$ is universal. We say that $\mathcal{S}$ is universal if any gate from $SU(d)$ can be built, with an arbitrary precision, using gates from $\mathcal{S}$, i.e. when the set of words in the alphabet $\mathcal{S}$ is dense in $SU(d)$. Universal quantum gates play an important role in quantum computing and quantum optics. The ability to effectively manufacture gates operating on many modes, using for example optical networks that couple modes of light, is a natural motivation to consider the universality problems not only for qubits but also for higher dimensional systems, i.e. qudits. It is known that for quantum computing with qudits, a universal set of gates consists of all one-qudit gates together with an additional two-qudit gate that does not map separable states onto separable states. The set of all one-qudit gates can be, however, generated using a finite number of gates $\mathcal{S}$. Interestingly, almost all sets of one-qudit gates are universal, i.e. non-universal sets $\mathcal{S}$ of the given cardinality are of measure zero. Surprisingly, however, it is hard to find operationally simple criteria that decide one-qudit gates universality. The main obstruction is the lack of classification of finite subgroups of $SU(d)$ for $d>4$.
The Solovay-Kitaev theorem states that all universal sets are roughly the same efficient. More precisely, the length of the word that is needed to approximate any gate $U\in SU(d)$ with the precision $\epsilon$ is bounded by $O(\log^c(1/\epsilon))$, where $c$ may depend only on $d$ and $c\geq 1$. Thus once we know that the set $\mathcal{S}$ is universal we also know it is efficiently universal. During my talk I will present an easy fast algorithm that allows deciding universality of an arbitrary set of one-qudit gates that works without knowing the classification of finite subgroups of $SU(d)$. More precisely, I will first provide compact form universality criteria that involve spectra of the gates and linear equations whose coefficients are polynomial in entries of the gates and their complex conjugates. They will be next used to build the universality checking algorithm that can be easily implemented numerically. The results concerning complexity of this algorithm, which I will discuss, show that the proposed approach allows fast detection of universal sets. Moreover, for non-universal $\mathcal{S}$ the presented criteria localise the reason of the non-universality and indicate what type of gates can be added to $\mathcal{S}$ to turn it into a universal set. The talk is based on the joint work with K. Karnas.
• Michal Oszmaniec. Universal extensions of restricted classes of quantum operations
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This provokes the question of what additional unitary gates should be added to a given gateset in order to attain physical universality, i.e., to be able to perform arbitrary unitary transformation on the relevant Hilbert space. In this work, we study this problem for three paradigmatic cases of naturally occurring restricted gatesets: (A) particle-number preserving bosonic linear optics, (B) particle-number preserving fermionic linear optics, and (C) general (not necessarily particle-number preserving) fermionic linear optics. Using tools from group theory and control theory, we classify, in each of these scenarios, what sets of gates are generated, if an additional gate is added to the set of allowed transformations. This allows us to solve the universality problem completely for arbitrary number of particles and for arbitrary dimensions of the single-particle Hilbert space.
• Daniel Jost Brod. A passive CPHASE gate via cross-Kerr nonlinearities
A fundamental and open question is whether cross-Kerr nonlinearities can be used to construct a controlled-phase (CPHASE) gate. In this talk, I describe a recent proposal for a gate constructed from a discrete set of atom-mediated cross-Kerr interaction sites arranged on a 1D array. One important aspect of our proposal is the use of counter-propagating wavepackets to reduce the spectral entanglement between the output photons. I will show how the average gate fidelity F between a CPHASE and our proposed gate increases as the number of interaction sites increases and the spectral width of the photon decreases, in particular obtaining > 99% fidelity with as few as 12 interaction sites. I will also discuss how our results shed light on the assumptions behind well-known no-go results.
• Fernando Brandão.Quantum Speed-ups for Semidefinite Programming
We present a new quantum algorithm for solving semidefinite programs. It gives a speed-ups over the best classical algorithm. We discuss applications to the problem of partial tomography of a quantum state.
• Stefan Boettcher.Determining the Efficiency of Quantum Search Algorithms with Renormalization
Quantum walks provide another powerful demonstration of the effectiveness of the renormalization group (RG), here applied to explore the origin of the computational complexity of quantum search algorithms. Grover’s abstract quantum search provides in principle a quadratic speed-up over the best classical algorithm in locating an element in an unsorted list. Implementations for such a search with coined quantum walks have been suggested that can nearly satisfy the Grover speed- limit for as low as a two-dimensional geometry. For these, the RG reveals a competition between Grover’s abstract algorithm, i.e., a rotation in Hilbert space, and quantum transport in an actual geometry. It can be characterized in terms of the quantum walk dimension d^Q_w and the spatial (fractal) dimension d_f , even when translational invariance is broken. The analysis simultaneously determines the optimal time for a quantum measurement and the likelihood for successfully pin- pointing the sought-after element in the list. Our RG considers entire families of problems to be studied, thereby establishing a large universality class for quantum search. Thus, the methods we propose open the door to a systematic study of universality classes in computational complexity and how a class may be broken to modify and control search behavior.
• Maxime Richard. Heat transfers in a nonequilibrium quantum fluid
Exciton-polaritons are low mass integer spin quasi-particles, that can be optically pumped in solid-state microcavities that are designed for this purpose. They are of mixed photonic and excitonic (bound electron-hole pair) nature and live only for a short time. In spite of this driven-dissipative nature, it has become quite clear over the last decade that polaritons constitute a unique experimental realization of a weakly interacting nonequilibrium quantum fluid, with defining phenomena such as condensation and superfluidity.
In this talk I will present some recent experimental work and their theoretical interpretation, in which a nonequilibrium polariton fluid is warmed-up by a genuine heat source, in a way that departs fundamentally from the equilibrium picture. We examine for instance how the thermal energy is accommodated by the condensate, by monitoring its spatial coherence, and how the nonequilibrium nature is a resource to dissipate this heat into the electromagnetic vacuum.
• Kavan Modi. Full and efficient characterisation of non-Markovian quantum processes
In science, we often want to characterise the processes undergone by a system of interest; this allows us to both identify the underlying physics driving the process and to predict what will happen to the system the next time the process occurs. If the state of the system at any time depends only on the state of the system at the previous time-step and some predetermined rule then these dynamics are characterised with relative ease. For instance, the dynamics of quantum mechanical systems in isolation is described in this way. But, when a quantum system repeatedly interact with an environment, the environment often ’remembers’ information about the system’s past. This leads to non-Markovian processes, which depend nontrivially on the state of the system at all times during its evolution and they are not, in general, be easily characterised using conventional techniques. Since the early days of quantum mechanics it has been a challenge to describe non-Markovian processes. Here we will show that using operational tools from quantum information theory we can fully characterise any non-Markovian process. In general the full characterisation is not efficient, as it requires exponentially large number of experiments. To overcome this obstacle we map the full process to a many-body state. We show that this can be achieved by using linear, in the number of time steps, amount of bipartite entanglement. Next, the state can be measured to any desired precision, thus the process can be characterised to any desired precision. Finally, we define a natural measure for the degree of non-Markovianity.
• Sebastião Pádua. Automated quantum operations in photonic qutrits
We develop a experimental optical setup capable of implementing a class of quantum operations in photonics qutrit states in transverse Gaussian paths variables. In order to implement a projection operation is necessary to be able, in principle, to transform an initial state that can be an one component state in a superposition of the others base states. The system that implements the operations needs to transform one photonic path state in a state of $D$ paths at the apparatus exit. Such transformation is difficult to be realized for slit states.
We present an experimental implementation of projection and permutation operations using photonic qutrit encoded in transverse Gaussian path states. Such experimental setup allows to obtain a qutrit state at the apparatus exit making them useful for a sequential quantum operation. The present operations are implemented exploring the diffraction of a Gaussian beam by a SLM due to a periodic phase modulation in it. We identify one set of diffraction phase grating for each operation realized, so the experiment is automated in the sense the operations are changed just by changing the SLM phase grating by a computer.
• Renné Medeiros de Araújo. Experimental study on Quantum Thermodynamics using Optical Vortices
Non-equilibrium thermodynamics and quantum information theory are interrelated research fields witnessing an increasing interest, both theoretical and experimental. This is manly due to the broadness of these theories, that found applications in many different fields of science, ranging from biology
to the foundations of physics. Here, by employing the orbital angular momentum of light, we propose a new platform for studying non-equilibrium properties of high dimensional quantum systems. Specifically, we use Laguerre-Gaussian beams to emulate the energy eigenstates of a two-dimension quantum harmonic oscillator having angular momentum. These light beams are subjected to a process realized by a spatial light modulator and the corresponding work distribution is experimentally reconstructed employing a two-point measurement scheme. The Jarzynski fluctuation relation is then verified. We also demonstrate the operation of the system as a Maxwell’s demon using post-selected data.
• Mateus Araújo. A purification postulate for quantum mechanics with indefinite causal order
To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.
• Fernando Parisio. Random measurements and nonlocality
Entanglement and nonlocality are distinct resources. It is acknowledged that a clear illustration of this point is the difference between maximally entangled states and states that maximally violate a Bell inequality. We give strong evidence that this anomaly may be an artifact of the measures that have been used to quantify nonlocality. By reasoning that the numeric value of a Bell function is akin to a witness rather than a quantifier, we define a measure of nonlocality and show that, for pairs of qutrits and of four-level systems, maximal entanglement does correspond to maximal nonlocality in the same scenario that gave rise to the discrepancy.In addition, we present an exhaustive numerical analysis of violations of local realism by families of multi- partite quantum states. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values, local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients.
• Yelena Guryanova. Connecting processes with multi-time quantum states : characterisations and resctrictions
We establish a direct connection between process matrices and the theory of multi-time quantum states. This offers a new conceptual point of view to the nature of process matrices. Our results also provide an explicit recipe to experimentally implement any process matrix in a probabilistic way, and allow us to generalize some of the previously known properties of process matrices. Furthermore, using this connection we investigate ideas related to closed time-like curves in these theories and find natural restrictions on their existence.
• Raphael Campos Drumond. Bounding entanglement spreading after a local quench
We consider the variation of von Neumann entropy of subsystems reduced states of general many-body lattice spin systems due to local quantum quenches. We obtain Lieb-Robinson-like bounds that are independent of the subsystem volume. The main assumptions are that the Hamiltonian satisfies a Lieb-Robinson bound and that the volume of spheres on the lattice grows at most exponentially with their radius. More specifically, the bound exponentially increases with time but exponentially decreases with the distance between the subsystem and the region where the quench takes place. The fact that the bound is independent of the subsystem volume leads to stronger constraints (than previously known) on the propagation of information throughout many-body systems. In particular, it shows that bipartite entanglement satisfies an
effective “light cone”, regardless of system size. Further implications to $t-$DMRG simulations of quantum spin chains and limitations to the propagation of information are discussed.
• Leandro Aolita. Fidelity witnesses for fermionic quantum simulations
The experimental interest in realizing quantum spin-1/2-chains has increased uninterruptedly over the last decade. In many instances, the target quantum simulation belongs to the broader class of non-interacting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally-friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.
• Dario Gerace. Steady state entanglement of spatially separated qubits
One of the pressing issues for the development of future quantum information technologies is the capability of initializing entangled qubits, and individually addressing them. While entanglement has been achieved in different technological platforms in the solid state, the demonstration of efficient entanglement between a pair of qubits separated by a spatially macroscopic distance has not been demonstrated on-chip, yet. Moreover, artificial atoms suffer from inherently short coherence times, which severely challenges their potential use as practical qubits.
In the first part of this talk, I will show how these artificially engineered qubits can be efficiently entangled, overcoming the dissipation by a continuous coherent driving with an external laser that produces a significant degree of steady state entanglement. A state-of-art technological platform based on semiconductor quantum dots coupled to photonic crystal dimers is proposed as the ideal system where such demonstration could be achieved in due time.
In the second part of the talk, I will address an elementary model of incoherently driven pair of artificial atoms, which is proposed as an autonomous quantum machine that is able to generate a significant amount of steady state entanglement without the need for any coherent driving. These results show that entanglement can arise in a driven-dissipative scenario only relying on incoherent energy sources. The basic model considered is a pair of qubits coupled to a quantized electromagnetic cavity mode: under specific conditions, the cavity mode provides an effective channel for mutual qubits interaction, which can be interpreted as dissipative bath engineering. Heat flowing through the system helps maintaining the non-local nature of the steady state. To make connection with the emerging field of quantum thermodynamics, we also provide a description of this microscopic device in terms of effective temperatures, which means that the device can work as a nanoscale thermal machine. More generally, this setup belongs to the class of autonomous quantum machines, since it can operate without any accurate external control on the dynamics. Moreover, we point out the possible role of non-local baths as a key ingredient for further developments in the design of quantum engines. Special attention is paid to realistic parameters in view of future tests and realizations in solid state systems.
• Elisa Bäumer. Work Extraction in Ion Traps
Motivation
According to Landauer’s Principle the erasure of one bit, i.e. resetting a bit in an unknown state to a well-known reference state, costs at least W=kTln2 work which is dissipated as heat into the environment at temperature T. In the opposite direction, using heat of a thermal bath at temperature T and the information of one initially pure qubit, one can extract at most W=kTln2 work while the qubit turns into a fully mixed state. Since the formulation of Landauer’s principle there have been experimental verifications in several set-ups, also in the quantum regime. However, only a few managed to explicitly store the extracted work and none were state-independent at the same time, that is, they all required to continuously track the state of the system. Our goal was to implement a state-independent protocol in trapped ions that explicitly stores the extracted work in a microscopic degree of freedom.
Theoretical Model & Experimental Realization
We formulate a protocol in the spirit of the thermal operations framework. In order to realize a work extraction protocol, we need three systems: a battery S of information qubits, a thermal bath B at fixed temperature T, modeled as a set of qubits in the Gibbs state, and a work storage system W. While the total system is subject to an energy-conserving unitary, we can use the information of one initially pure battery qubit S to convert heat from the coupled thermal bath B into work stored in system W. In the experiment, the battery qubit S and thermal qubit B are represented by the internal states of two ions, while the work storage system W is represented by a common motional mode of these two ions. The unitary is achieved by a composition of Pi-pulses, Molmer-Sorensen gates and Red Sideband Transformations.
Contribution & Outlook
In collaboration with J. Home’s Trapped Ion group (ETH Zurich) we developed a protocol for trapped ions that explicitly stores the extracted work in the motional mode of two trapped ions and that runs state-independently. We analyzed the energy fluctuations during the evolution and used simulations to estimate the errors. The protocol is experimentally feasible and its implementation in the Trapped Ion group will be carried out during the next months.
• Paul Erker. Autonomous quantum clocks: how thermodynamics limits our ability to measure time
Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here we explore these questions by introducing a model of time measurements that is complete and self-contained. Specifically, our autonomous quantum clock consists of a system out of equilibrium — a prerequisite for any system to function as a clock — powered by minimal resources, namely two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of *any* autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.
• Rosanna Nichols. Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift φ whose generator is randomly sampled according to a distribution with unknown concentration κ, which introduces a physical source of noise. We then investigate strategies for the joint estimation of the two parameters φ and κ given a finite number N of interactions with the phase imprinting channel. We consider both single qubit and multipartite entangled probes, and identify regions of the parameters where simultaneous estimation is advantageous, resulting in up to a twofold reduction in resources. Quantum enhanced precision is achievable at moderate N, while for sufficiently large N classical strategies take over and the precision follows the standard quantum limit. We show that full-scale entanglement is not needed to reach such an enhancement, as efficient strategies using significantly fewer qubits in a scheme interpolating between the conventional sequential and parallel metrological schemes yield the same effective performance. These results may have relevant applications in optimization of sensing technologies.
• Fabricio Toscano. Attainability of the quantum information bound in pure state models.
The attainability of the quantum Cramér-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher information associated to a given measurement on the quantum state of a system which encodes the information about the parameter coincides with the quantum Fisher information associated to that quantum state. Braunstein and Caves [PRL {\bf 72}, 3439 (1994)] have shown that the QIB can always be achieved via a projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. However, such projective measurement depends, in general, on the value of the parameter to be estimated. Requiring, therefore, the previous knowledge of the quantity one is trying to estimate. For this reason, it is important to investigate under which situation it is possible to saturate the QCR without previous information about the parameter to be estimated.
Here, we show the complete solution to the problem of which are all the initial pure states and the projective measurements that allow the global saturation of the QIB, without the knowledge of the true value of the parameter, when the information about the parameter is encoded in the system by a unitary process.
• Gabriel Aguilar. Quantum teleportation across a metropolitan fibre network
If a photon interacts with a member of an entangled photon pair via a so-called Bell-state measurement (BSM), its state is teleported over principally arbitrary distances onto the second member of the pair. Starting in 1997, this puzzling prediction of quantum mechanics has been demonstrated many times; however, with one very recent exception, only the photon that received the teleported state, if any, travelled far while the photons partaking in the BSM were always measured closely to where they were created. Here, using the Calgary fibre network, we report quantum teleportation from a telecommunication-wavelength photon, interacting with another telecommunication photon after both have travelled over several kilometres in bee-line, onto a photon at 795~nm wavelength. This improves the distance over which teleportation takes place from 818~m to 6.2~km. Our demonstration establishes an important requirement for quantum repeater-based communications and constitutes a milestone on the path to a global quantum Internet.
• Juan Bermejo-Vega. Contextuality as a resource for qubit quantum computation
A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wavefunctions.The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation. Last, we extend our techniques to devise an (improved) proof that contextuality is a necessary resource in all odd qudit dimensions.
• Carmine Napoli. Towards quantum super-resolution in estimating angular and axial separations
Rayleigh’s criterion for two incoherent point sources has been the milestone for optical resolution since its formulation. It amounts to the classical Cramér-Rao lower bound on the mean-squared error of any unbiased estimator of the separation of the sources using photon counting on the image plane. Recent works have shown that a universal limit to optical resolution is given by the quantum CramérRao bound, yielding a mean-squared error that is inversely proportional to the quantum Fisher information and stays finite at arbitrary separation, beating «Rayleigh’s curse»
• Elizabeth Agudelo. Nonclassicality in Hybrid Systems
We discuss different notions of quantum correlations in composite systems. We investigate how they extend to the joint description of hybrid systems, based on different definitions of quantumness related to its individual subsystems. A bipartite case is analytically characterized, we combine one continuous-variable harmonic oscillator and one discrete-variable qubit subsystem. The connection of two typically applied and distinctively different concepts of nonclassicality in quantum optics and quantum information is established. Our investigation includes the representation of correlated states in terms of quasiprobability matrices. In order to verify the nonclassicality present on the quasiprobability matrices, a matrix version of a nonclassicality quasiprobability is derived. Negative eigenvalues of this matrix are necessary and sufficient to visualize any multipartite quantum correlation present in the physical system and they can be directly sampled.
We also make a comparative study of joint and conditional quantum correlations. We analyze nonclassical correlations in connection to the joint and conditional probability distributions of the measurement outcomes of some particular observables. It is demonstrated that joint and conditional variances of the same observable and the same state can be sensitive to different forms of nonclassicality.
• Roberto Serra. Experimental rectification of entropy production by a Maxwell’s Demon in a quantum system
Connections between thermodynamics and information theory have been producing important insights and useful applications in the past few years, which has turned out to be a dynamic field. Its genesis traces back to the famous Maxwell’s demon gedanken experiment. In 1867, Maxwell conceived a “neat fingered being,” which has the ability to gather information about the microscopic state of a gas and use this information to transfer fast particles to a hot medium and slow particles to a cold one, engendering an apparent conflict with the second law of thermodynamics. Several approaches and developments concerning this conundrum had been put forward, but only after more than a century, in 1982, Bennett realised that the apparent contradiction with the second law could be puzzled out by considering the Landauer’s erasure principle. Maxwell’s demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this “intelligent observer” is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwells demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This implementation provides experimental evidence that the irreversibility in a non-equilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
• Alexia Auffeves. Rebuilding quantum thermodynamics on quantum measurement
Thermodynamics relies on randomness. In classical thermodynamics, the coupling to a themral bath induces stochastic fluctuations on the system considered: Thermodynamic irreversibility stems from such fluctuations [1], which also provide the fuel of thermal engines. Quantum theory has revealed the existence of an ultimate source of randomness: Quantum measurement through the well-known measurement postulate [2]. In this talk I will present recent attempts to rebuild quantum thermodynamics on quantum measurement, from quantum irreversibility to quantum engines extracting work from quantum fluctuations [3,4].

[1] A. Auffèves, Viewpoint : Nuclear spin points out the arrow of time, Physics 8, 106 (2015)
[2] A. Auffèves, P. Grangier, Recovering the quantum formalism from physically realist axioms, Scientific Reports 43365 (2017)
[3] C. Elouard, D. Herrera-Marti, M. Clusel, A. Auffèves, The role of quantum measurement in stochastic thermodynamics, npj QI 10.1038 (2017)
[4] C. Elouard, D. Herrera-Marti, B. Huard, A. Auffèves, Extracting work from quantum measurement in Maxwell’s demon engines, Phys. Rev. Lett. 118, 260603 (2017), featured in Phys.org and Nature Research Highlights