Speaker: Pedro Lamberti ( Jagiellonian University/ University of Cordoba, Argentina )
Jensen–Shannon divergence is an important distinguishability measure between probability distributions that finds interesting applications within the context of Information Theory. In particular, this classical divergence belongs to a remarkable class of divergences known as Csiszár or f -divergences. In this talk I analyze the problem of obtaining a distance measure between two quantum states starting from the classical Jensen–Shannon divergence between two probability distributions. Considering the Jensen–Shannon divergence as a Csiszár divergence, I first focus on the problem of distinguishability between two pure quantum states. It is found a quantum version of the classical Jensen–Shannon divergence that differs from the previously introduced Quantum Jensen–Shannon Divergence. The two quantum versions of Jensen–Shannon divergence have different interpretations within the framework of Quantum Information Theory. Whereas the former quantum version of Jensen–Shannon divergence can be interpreted as the Holevo bound, the alternative quantum version obtained in this work equals the accessible information. Furthermore, it is obtained a monoparametric family of metrics between two quantum pure states. Finally, it is presented an extension of this family of metrics to the case of mixed quantum states by means of the concept of purification.
Atom interferometry for extended drift times promise a major leap in improving precision and accuracy of matter-wave sensors. When taking advantage of the unique space environment for example, fundamental tests challenging the state-of-the-art can be performed using quantum gases systems. The use of cold atoms as a source for such sensors poses however intrinsic challenges mainly linked to the samples size and mixture dynamics in case of dual-atomic tests. In this context, the design of the input states with well-defined initial conditions is required. In this talk, I will report about quantum state engineering methods used to precisely and efficiently control the positions, velocities, expansion rates and squeezing of atomic ensembles in state-of-the-art quantum gas experiments on ground and in space.
Quantifying non-classicality via Local Operations and Shared Randomness
Date: Monday, May 9, 2022
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
In this talk I will motivate Local Operations and Shared Randomness (LOSR) as a paradigm to quantify non-classical resources, in contrast to Local Operations and Classical Communication (LOCC). I will provide examples of the resource-theoretic study of entanglement, Bell non-classicality, and Einstein-Podolsky-Rosen steering, that stems from this LOSR approach. In particular, I’ll discuss how this triggers a whole distinct new branch of entanglement theory.
Signatures of nonclassicality in quantum mechanical and optical systems
In this talk I will present a brief summary of my habilitation works concerning four aspects of nonclassicality: quantum entanglement,
indistinguishability of quantum particles, Bell nonclassicality and contextuality.
Thirty-six entangled officers of Euler: quantum solution of a classically impossible problem
Speaker: Karol Życzkowski (CFT, PAS and Jagiellonian University)
Classical combinatorial designs are composed of elements of a finite set and arranged with a certain symmetry and balance. A simple example of a combinatorial design is given by a single Latin square: square array of size d filled with d copies of d different symbols, each occurring once in each row and in each column. Such patterns are useful in statistics to design optimal experiments.
Analogous collections of quantum states, called a quantum design, determine distinguished quantum measurements and can be applied for various purposes of quantum information processing. Negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum Latin squares of this size. The solution can be visualized on a chessboard of size six, which shows that 36 officers are split in nine groups, each containing of four entangled states.
As a consequence, we find an example of Absolutely Maximally Entangled (AME) state of four subsystems with six levels each, which deserves the appellation golden AME state, as the golden ratio appears prominently in its elements. This state enables us to construct a pure nonadditive quhex quantum error detection code, which allows one to encode a 6-level state into a triplet of such states. Furthermore, using such a state one can teleport any unknown, two-dice quantum state, from any two owners of two subsystems to the lab possessing the two other dice forming the four-dice system.
 S.A Rather, A.Burchardt, W. Bruzda, G. Rajchel-Mieldzioć, A. Lakshminarayan and K. Życzkowski, Thirty-six entangled officers of Euler, Phys. Rev. Lett. 128, 080507 (2022).
 D. Garisto, Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution, Quanta Magazine, Jan. 10, 2022; https://www.quantamagazine.org/
 Ph. Ball, A Quantum Solution to an 18th-Century Puzzle, Physics, 15, 29 (2022); https://physics.aps.org/articles/v15/29
 K. Życzkowski, W. Bruzda, G. Rajchel-Mieldzioć, A.Burchardt, S.A Rather, A. Lakshminarayan, 9 × 4 = 6 × 6: Understanding the quantum solution to the Euler’s problem of 36 officers, preprint https://arxiv.org/abs/2204.06800
Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
Date: Monday, April 25, 2022
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Speaker: Katarzyna Roszak (Institute of Physics, Czech Academy of Sciences)
We provide a proof that entanglement of any density matrix which block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can simply be calculated as the weighted average of entanglement present within each block. This is especially useful for thermal-equilibrium states which always inherit the symmetries present in the Hamiltonian, since block-diagonal Hamiltonians are common as are interactions which involve only a single degree of freedom of a greater system. We exemplify our method on a simple Hamiltonian, showing the diversity in possible temperature-dependencies of Gibbs state entanglement which can emerge in different parameter ranges.
Quantum mechanics is at its hearts the study of nature at the fundamental level of atoms and subatomic particles. Made up of these same atoms and subatomic particles, biological systems are also expected to follow quantum mechanics to some extent. The most well-known example (and still debated) is in magnetoreception, where some animals are thought to use magnetically sensitive chemical dynamics as compasses to obtain directional information from the Earth’s magnetic field. This process involves the electron spins and quantum coherences of the intermediate “radical pairs” reactants. I will give an overview of two experiments performed that investigate quantum effects in animals. Firstly, we show that the magnetic sensitivity of Periplaneta americana, the American cockroach, confirmed in behavioural experiments is most likely based on the radical pair compass. In the second experiment, we describe measurements on a qubit-qubit-tardigrade system and observe a coupling between the animal in the tun state and a qubit. Further steps and quantum state tomography on the total system shows non-zero tripartite entanglement. Finally, the tardigrade was shown to properly revive after being placed back at room temperature water. The two experiments show that biological systems can be bridged with quantum mechanics and will be relevant in probing the limits of quantum to classical transitions.
Genuine multipartite entanglement and nonlocality in pair-entangled network states
Date: Wednesday, April 20, 2022
Host: Quantum Information and Quantum Computing Working Group (CTP PAS)
Speaker: Julio de Vicente (Universidad Carlos III de Madrid)
The study of entanglement and nonlocality in multipartite quantum states plays a major role in quantum information theory and genuine multipartite entanglement (GME) and nonlocality (GMNL) signal some of its strongest forms for applications. However, their characterization for general (mixed) states is a highly nontrivial problem and its experimental preparation faces the formidable challenge of controlling quantum states with many constituents. In this talk I introduce a subclass of multipartite states, which I term pair-entangled network (PEN) states, as those that can be created by distributing exclusively bipartite entanglement in a connected network, and I study how their entanglement and nonlocality properties are affected by noise and the geometry of the graph that provides the connection pattern. The motivation is twofold. First, this class represents arguably the most feasible way to prepare GME and GMNL states in practice. Second, the class of PEN states provides an operationally motivated subset of multipartite states in which the well-developed theory of bipartite entanglement can be exploited to analyze entanglement in the multipartite scenario. I will show that all pure PEN states are GME and GMNL independently of the amount of entanglement shared and the network (as long as it is connected). In contrast, in the case of mixed PEN states these properties depend both on the level of noise and the network topology and they are not guaranteed by the mere distribution of mixed bipartite entangled states. In particular, the amount of connectivity in the network determines whether GME is robust to noise for any system size or whether it is completely washed out under the slightest form of noise for a sufficiently large number of parties. This latter case implies fundamental limitations for the application of certain networks in realistic scenarios, where the presence of some form of noise is unavoidable. In addition to this, if time allows, to illustrate the applicability of PEN states to study the complex phenomenology behind multipartite entanglement I will present three more results which use them as a proof ingredient: (i) all pure GME states are GMNL in the multiple-copy scenario, (ii) GMNL can be superactivated for any number of parties, and (iii) the set of GME-activatable states can be characterized as those states that are not partially separable.
Quantum reference frames: towards a quantum description of space and time
In physics, observations are typically made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in practical situations it is a physical system that constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? In the talk, I will introduce a general method to associate a reference frame to a quantum system, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. Such quantum reference frames transformations imply that the notion of entanglement and superposition are not given a priori, but depend on the choice of the quantum reference frame even in a non-relativistic setting. Quantum reference frames could be a useful tool at the intersection of gravity and quantum theory: for instance, they allow one to generalise Einstein’s equivalence principle to superpositions of gravitational fields, and to describe the behaviour of quantum clocks ticking in a superposition of times relative to one another.
Physics and Metaphysics of Wigner’s Friends
Date: Monday, April 11, 2022
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Speaker: Marcin Markiewicz ( University of Gdańsk )
Recently there appeared many works on modified Wigner’s Friend paradoxes, which suggest that quantum theory cannot consistently describe the scenario with many observers. In this presentation I will show an alternative approach to this problem, which indicates that the paradoxes are in fact apparent, and the source of confusion is the undefined status of the measurement process. The talk will be based on recently published work “Physics and Metaphysics of Wigner’s Friends: Even Performed Premeasurements Have No Results” by Marek Żukowski and Marcin Markiewicz, Phys. Rev. Lett. 126, 130402 (2021).
Degradation of the resource state in the deterministic port-based teleportation scheme
Port-based teleportation (PBT) is a quantum teleportation protocol, in which the parties exploit joint measurements performed on $N$ shared $d$-dimensional maximally entangled pairs (the resource) and the state to be teleported, with the addition of the one-way classical communication. The lack of correction in the last step is an essential feature distinguishing PBT from standard quantum teleportation. In my talk I shall consider the idea of entanglement recycling, i.e. the repeated use of the same resource for multiple rounds of PBT. The question is how the resource degrades after one or multiple uses. To answer it, we analyse the structure of the measurement employed in the protocol (the square-root-measurement, to be precise), depending greatly on the symmetries present in the system. In particular, as the result we evaluate its roots and compositions. These findings allow us to present the explicit formula for the recycling fidelity involving only group-theoretic parameters describing irreducible representations of the symmetric group $S(n)$. Additionally, I shall present the analysis of the resource degradation in the optimal PBT.