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Workshop on "Probabilistic techniques and Quantum Information Theory"

`The conference will be held in the Institut Henri Poincaré, 23-27 October 2017

Organizers

Confirmed Speakers
  1. Antonio Acín (ICFO Barcelona)
  2. Radosław Adamczak (University of Warsaw)
  3. Rotem Arnon-Friedman (ETH Zürich)
  4. Benoit Collins (Kyoto University and CNRS)
  5. Nilanjana Datta (Cambridge University)
  6. Motohisa Fukuda (Yamagata University)
  7. Carlos González-Guillén (Universidad Politécnica de Madrid)
  8. Razvan Gurau (CPHT, Ecole Polytechnique)
  9. Madalin Guta (University of Nottingham)
  10. Teiko Heinosaari (Turku University)
  11. Ke Li (Caltech)
  12. Satya Majumdar (LPTMS Orsay)
  13. Camille Male (Université de Bordeaux)
  14. Sho Matsumoto (Kagoshima University)
  15. James Mingo (Queen's University)
  16. Ashley Montanaro (University of Bristol)
  17. Ramis Movassagh (IBM TJ Watson Research Center)
  18. Yan Pautrat (Université Paris-Sud)
  19. Zbigniew Puchała (IITIS, Gliwice, Poland)
  20. Roland Speicher (Saarland University)
  21. Yoshimichi Ueda (Kyushu University)
  22. Ping Zhong (Waterloo University)

Schedule
TBA

Talks
  • Antonio Acín - Non-commutative polynomial optimisation problems in quantum information theory
    We discuss questions in quantum physics that can be cast as non-commutative polynomial optimisation problems and discuss their solution in terms of semi-definite programming. This ranges from new approaches to detect entangled states to the computation of ground state energies of interacting systems. We argue that these methods can play an important role for the certification of quantum effects.

  • Radosław Adamczak - Entropic and metric uncertainty relations for random unitary matrices
    I will discuss recent results concerning almost optimal entropic and metric (total-variation and Hellinger) uncertainty relations which hold with high probability for measurements given by i.i.d. Haar distributed random unitary matrices. If time permits I will also discuss some applications to information locking and data hiding. The talk will be partially based on joint work with Rafal Latala, Zbigniew Puchala and Karol Zyczkowski.

  • Rotem Arnon-Friedman - Simple and tight device-independent security proofs
    Device-independent (DI) cryptography aims at achieving security that holds irrespective of the quality, or trustworthiness, of the physical devices used in the implementation of the protocol. Such a surprisingly high level of security is made possible due to the phenomena of quantum non-locality. The lack of any a priori characterisation of the device used in a DI protocol makes proving security a challenging task. Indeed, proofs for, e.g., DI quantum key distribution (DIQKD) were only achieved recently and result in far from optimal key rates while being quite complex.
    In this talk I will explain how a newly developed tool, the “entropy accumulation theorem” of Dupuis et al., can be effectively applied to give fully general proofs of DI security that yield essentially tight parameters for a broad range of DI tasks. At a high level our technique amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This makes the proof much simpler and allows us to achieve significantly better quantitative results for the case of general quantum adversaries. As concrete applications I will present simple and modular security proofs for DIQKD and randomness amplification.  

  • Nilanjana Datta - Concentration of quantum states from quantum functional and Talagrand inequalities
    Quantum functional inequalities (e.g. the logarithmic Sobolev- and Poincaré inequalities) have found widespread application in the study of the behavior of primitive quantum Markov semigroups. The classical counterparts of these inequalities are related to each other via a so-called Talagrand inequality of order 2 (T2). The latter inequality relies on the notion of a metric on the set of probability distributions called the Wasserstein distance of order 2. (T2) in turn implies a Talagrand inequality of order 1 (T1). In this paper, we introduce quantum generalizations of the inequalities (T1) and (T2), making use of appropriate quantum versions of the Wasserstein distances, one recently defined by Carlen and Maas and the other defined by us. We establish that these inequalities are related to each other, and to the quantum modified logarithmic Sobolev- and Poincaré inequalities, as in the classical case. We also show that these inequalities imply certain concentration-type results for the invariant state of the underlying semigroup. We consider the example of the generalized depolarizing semigroup to derive concentration inequalities for any finite dimensional full-rank quantum state. These inequalities are then applied to derive upper bounds on the error probabilities occurring in the setting of finite blocklength quantum parameter estimation. This is joint work with Cambyse Rouzé.

  • Satya Majumdar - Number fluctuations and entanglement entropy for trapped Fermi gases

  • Sho Matsumoto - Overview of Weingarten calculus for classical groups and symmetric spaces
    Weingarten calculus, triggered by Weingarten's paper (1978), is a general method for computations of integrals of polynomial functions on compact Lie groups and symmetric spaces. It has been widely applied to classical/free probability, representation theory, random matrix theory, and others. Especially, it is useful for Quantum Information Theory. I explain various formulas in Weingarten calculus, developed by Benoit Collins and his collaborators including me. Our approach is based on harmonic analysis and combinatorics for symmetric groups.

  • Ashley Montanaro - Probabilistic techniques for simulating quantum computational supremacy experiments
    The fast pace of recent experimental developments has led to the hope that quantum computers will soon demonstrate computational performance far beyond classical computers: a milestone known as quantum (computational) supremacy. However, the relative simplicity of near-term experiments leaves open the possibility that they could be simulated classically more easily than full quantum computers could.
    In this talk, I will discuss two such classical simulation results for proposed architectures for quantum computational supremacy experiments. The first is a classical algorithm for simulating certain noisy commuting quantum computations ("IQP circuits") in polynomial time, based on Fourier analysis over Z_2^n. The second is experimental work demonstrating that simple probabilistic methods can be used to simulate boson sampling experiments significantly more efficiently than previously thought. This implies that quantum computational supremacy is unlikely to be achieved via boson sampling in the near future.
    The talk is based on joint work with Michael Bremner and Dan Shepherd (Quantum 1, 8 (2017); arXiv:1610.01808), and joint work with Alex Neville, Chris Sparrow, Raphael Clifford, Eric Johnston, Patrick Birchall and Anthony Laing (arXiv:1705.00686).

  • Zbigniew Puchała - Asymptotic properties of random quantum states and channels
    Properties of random mixed states of dimension N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N, due to the concentration of measure phenomenon, the trace distance between two random states tends to a fixed number 1/4+1/π, which yields the Helstrom bound on their distinguishability. To arrive at this result we apply free random calculus and derive the symmetrized Marchenko-Pastur distribution. We consider also random quantum channels, especially the limiting behaviour of the diamond norm for two independent random quantum operations. In the case of flat measure on random channels, the limiting value of the diamond norm is equal to 1/2+2/π.

  • Ping Zhong - Some noncommutative probability aspects of meandric systems
    The talk will consider a family of diagrammatic objects (well-known to combinatorialists and mathematical physicists) which go under the names of ”meandric systems” or ”semi-meandric systems”. I will review some connections which these objects are known to have with free probability, and I will show in particular how the so-called ”semi-meandric polynomials” can be retrieved from a natural consideration of operators on the q-Fock space. This is joint work with Alexandru Nica.