15th CEQIP workshop, June 13-16 2018, Smolenice, Slovakia

  1. Matthias Kleinman: Methods for a conclusive verification of bipartite bound entanglement   ΞΞΞ Bipartite bound entangled states form a class of states with a small volume within the quantum states. Also, this class of states is particularly difficult to prepare experimentally, because bound entangled states are both, entangled and mixed. Even if data has been taken successfully, yet another challenge is the actual verification that such a preparation was successful, since all states compatible with the data have to be verified to be bound entangled. In this talk I will present a method to find states which are most suitable for preparation and verification and I detail the statistical methods for verifying that the experimental state was indeed bound entangled.
  2. Tamás Vértesi: Useful correlations from bound entangled states   ΞΞΞ Bound entangled states are very weakly entangled states. In fact they are so weakly entangled that given an infinite number of copies, no pure state entanglement can be distilled from them. Nevertheless, they are useful in certain applications such as quantum key distribution. Here we show that bipartite bound entangled states are also useful in metrology and Bell nonlocality. In particular they can outperform separable states in linear interferometers and can give rise to Bell inequality violation.
  3. Sergii Strelchuk: Learning hard quantum distributions with variational autoencoders ΞΞΞStudying general quantum many-body systems is one of the major challenges in modern physics because it requires computational resources that scale exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. In my talk, I will introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. We focus on two questions: (i) Are deeper networks better at learning quantum states? (ii) How well can we learn "hard" states? I will review recent mathematical results which explore how depth improves the representational capability of networks for classical problems and discuss our results for the quantum case.
  4. Marcus Huber: Thermodynamic limitations to quantum measurements   ΞΞΞ Projective measurements and the Born rule are centerpieces of the foundation of quantum information theory. They do, however, seem to violate the third law of thermodynamics. We show that in a self-contained description, quantum measurements are indeed strictly speaking impossible and can only be approximated at a work cost that diverges with the desired quality of the measurement approaching perfection. We then build an explicit model for a self contained measurement and show that reasonable measurements of quantum systems require macroscopic units of energy in order to be realised.
  5. Robert Koenig: Quantum advantage with shallow circuits   ΞΞΞ We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An instance of the problem is specified by a quadratic form q that maps n-bit strings to integers modulo four. The goal is to identify a linear boolean function which describes the action of q on a certain subset of n-bit strings. We prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the 2D Hidden Linear Function problem with high probability must have depth logarithmic in n. In contrast, we show that this problem can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates acting locally on a two-dimensional grid. This is joint work with Sergey Bravyi and David Gosset.
  6. Alessandro Bisio: Higher order quantum computation   ΞΞΞ Higher order quantum computation is an extension of quantum computation where input and output of transformations can be transformations themselves. This idea leads to the notion of higher order maps, which generalise channels and quantum operations. Such a generalisation goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher order maps, exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. Higher order quantum computation is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms for higher order computation do not refer to the specific mathematical structure of quantum theory, and can be therefore exported in the context of any general operational probabilistic theory.
  1. Sergey Filippov: Lower and upper bounds on classical capacity of nonunital channels
  2. Andreas Bluhm: Quantum compression relative to a set of measurements
  3. Stefan Baeuml: Fundamental limitations on the capacities of bipartite quantum interactions
  4. Frédéric Dupuis: Secure Certification of Mixed Quantum States with Application to Two-Party Randomness Generation
  5. Daniel Nagaj: Shorter unentangled proofs for Ground State Connectivity
  6. Remigiusz Augusiak: Bell inequalities for maximally entangled states
  7. Chris Perry: Elementary Thermal Operations
  8. Aleksandra Krawiec: Vertices cannot be hidden from quantum spatial search for almost all random graphs
  9. Miguel Navascues: Resetting uncontrolled quantum systems
  10. Jedrzej Kaniewski: Self-testing of qutrit systems
  11. Vilasini Venkatesh: Composable security in relativistic quantum cryptography
  12. Zbigniew Puchała: Coherifying quantum channels
  13. Marti Perarnau-Llobet: Quantum metrology with one-dimensional superradiant photonic states
  14. Libor Caha: Feynman-Kitaev computer's clock: bias, gaps, idling and pulse tuning
  15. Wieslaw Laskowski: Multipartite nonlocality and random measurement
  1. Fabian Bernards: On the Generalisation of Daemonic Gain in Ergotropy
  2. Konstantin Beyer: Dynamical quantum steering of an open qubit
  3. Jakub Jan Borkala: Multiparty Distributed Quantum Random Access Codes
  4. Tom Bullock: Characterising Optimal Error Bounds for Qubits
  5. Mikołaj Czechlewski: Efficient device independent dimension witness of arbitrary quantum systems employing binary outcome measurements
  6. Shin-Liang Chen: Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
  7. Máté Farkas: Self-testing mutually unbiased bases in the prepare-and-measure scenario
  8. Piotr Gawron: Hyper-spectral image segmentation using adiabatic quantum computation
  9. Antonio Sebastian Rosado González: The effect of Lorentz transformations on quantum observables and reduced density matrices
  10. Felix Huber: Exponentially many monogamy and correlation constraints for multipartite states
  11. Tomasz Januszek: Impact of global and local interaction on quantum spatial search on chimera graph
  12. Niklas Johansson: Efficient simulation of some quantum computer algorithms
  13. Mátyás Koniorczyk: Nonlocal behaviors and game-theoretic narratives
  14. Ryszard Kukulski: Strategies for optimal single-shot discrimination of quantum measurements
  15. Dariusz Kurzyk: Unconditional Security of a K-State Quantum Key Distribution Protocol
  16. Paulina Lewandowska: Monotonicity of the average singular values of Ginibre matrices
  17. Justyna Łodyga: Do closed timelike curves violate the second law of thermodynamics?
  18. Edgar Aguilar Lozano: Randomness Certification Under Realistic Assumptions
  19. Kimmo Luoma: Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics
  20. Ludek Matyska: Tomography of unitary and random unitary
  21. Nikolai Miklin: Causal inequalities from variable-elimination methods
  22. Piotr Mironowicz: Connections Between Mutually Unbiased Bases and Quantum Random Access Codes
  23. Nikolay Nahimovs: On the Probability of Finding Marked Connected Components Using Quantum Walks
  24. Mateusz Ostaszewski: Geometrical versus time-series representation of data in learning quantum control
  25. Jaroslav Pavličko: Equivalence of programmable quantum processors
  26. Łukasz Pawela: Spectrum broadcast structures in spin star systems
  27. Matej Pivoluska: Tensor valued hypergraph states
  28. Martin Plávala: Conditions for the compatibility of channels and their connection to steering and Bell nonlocality
  29. Martin Plesch: Loss of Information in Quantum Guessing Game
  30. Constantino Rodriguez Ramos: Convex structure of the set of doubly-stochastic qutrit quantum channels.
  31. Peter Rapčan: Area-law entangled eigenstates can preserve ergodicity
  32. Daniel Reitzner: Grover Search under Localized Dephasing
  33. Tomas Rybar: Memory requirements for general reversible qubit stream processors
  34. Michal Sedlak: Perfect probabilistic storing and retrieving of unitary channels
  35. Timo Simnacher: Entanglement detection with scrambled data
  36. Anna Szczepanek: Dynamical entropy for qutrits: beyond rank-one POVMs
  37. Iskender Yalcinkaya: Ideal negative measurements for a photonic quantum walk
  38. Xiao-Dong Yu: Detecting Coherence via Spectrum Estimation
  39. Yichen Zhang: Noiseless Linear Amplifiers in Continuous Variable Measurement Device Independent Quantum Cryptography
  40. Mario Ziman: Equivalence of programmable quantum processors (⇒ No.25)
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