Quantum Seminar

2020:
 

Title: Tsirelson-Connes reading group

Time: Thursday June 18th at 10am

Place: Online

Speaker: Laurent Bartholdi (Georg-August University, Göttingen)

Abstract: Low-degree testing


Title: Optimal symmetric cloning of pure states

Time: Wednesday June 10th at 10am

Place: Online

Speaker: Denis Rochette (Toulouse)

Abstract: Continuing our series on representation theory and quantum information


Title: Tsirelson-Connes reading group

Time: Thursday May 28th at 10am

Place: Online

Speaker: Bruno Sévennec (CNRS, UMPA Lyon)

Abstract: Around the PCP theorem


Title: Representation Theory and Quantum Information

Time: Wednesday May 27th at 10am

Place: Online

Speaker: Hoang and Shang-Chun

Abstract: Continuing our series on representation theory and quantum information, Hoang and Shang-Chun will present the paper https://arxiv.org/abs/quant-ph/0409016 next wednesday.


Title: Tsirelson-Connes reading group

Time: Thursday May 7th at 10am

Place: Online

Speaker: Sophie Morel (CNRS, UMPA Lyon)

Abstract: Robust self-testing via approximate representations


Title: Compatibility of quantum measurements and inclusion of free spectrahedra

Time: Wednesday May 6th at 10am

Place: Online

Speaker: Ion Nechita (CNRS, Toulouse)

Abstract: I will relate the problem of determining whether a given set of quantum measurements is compatible to the inclusion of free spectrahedra. We show how results from algebraic convexity can be used to quantify the degree of incompatibility of binary quantum measurements. In particular, this new connection will allow to completely characterize the case in which the dimension of the quantum system is exponential in the number of measurements.


Title: Tsirelson-Connes reading group

Time: Thursday April 30th at 10am

Place: Online

Speaker: Cécilia Lancien (CNRS, IMToulouse)

Abstract: Exact self-testing for binary constraint system games : In this talk I will start with explaining the concept of self-testing (aka rigidity) for non-local games. I will then present a general approach which allows to prove self-testing results for a class of games known as binary linear system games, through the representation theory of their so-called solution group. This talk will be mostly based on ideas and results appearing in https://arxiv.org/abs/1606.02278 and https://arxiv.org/abs/1709.09267.


Title: Quantum Polar Codes

Time: Wednesday April 29th at 10am

Place: Online

Speaker: Mehdi Mhalla (LIG Grenoble)

Abstract: https://arxiv.org/abs/1904.04713


Title: Optimal Channel Coding from a Geometric Point of View

Time: Monday April 20th at 10am

Place: Online

Speaker: Paul Fermé

Abstract:


Title: Tsirelson-Connes reading group

Time: Thursday April 16th at 10am

Place: Online

Speaker: Omar Fawzi

Abstract: From the game compression procedure to the undecidability of approximating the quantum value of a game


Title: Tsirelson-Connes reading group

Time: Thursday April 9th at 10am

Place: Online

Speaker: Guillaume Aubrun and Omar Fawzi

Abstract: A convergent hierarchy of computable upper bounds on the entangled value of a game (https://arxiv.org/abs/0803.4290)


Title: Introduction to representation theory and Schur Weyl duality (Part 2 : Schur Weyl duality)

Time: Monday April 6th at 10am

Place: Online

Speaker: Aadil Oufkir

Abstract: 


Title: Tsirelson-Connes reading group

Time: Thursday April 2nd at 10am

Place: Online

Speaker: Etienne Moutot

Abstract: Machines de Turing et calculabilité


Title: Quantum Pin Codes

Time: Friday March 13th at 10:15

Place: Salle de Réunion du M7, ENS de Lyon (Site Monod)

Speaker: Christophe Vuillot (Inria Paris)

Abstract: We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a vast generalization of quantum color codes and Reed-Muller codes. A lot of the structure and properties of color codes carries over to pin codes. Pin codes have gauge operators, an unfolding procedure and their stabilizers form multi-orthogonal spaces. This last feature makes them interesting for devising magic-state distillation protocols. We study examples of these codes and their properties. (https://arxiv.org/abs/1906.11394)


Title: Tsirelson-Connes reading group

Time: Thursday Feb 20th at 10:15

Place: Salle 435, ENS de Lyon (Site Monod)

Speaker: Alexander Müller-Hermes and Emilie Mai Elkiaer

Abstract: The set of quantum correlations is not closed, arXiv:1703.08618 et arXiv:1709.05032.


Title: Tsirelson-Connes reading group

Time: Thursday Feb 13th at 10:15

Place: Salle 435, ENS de Lyon (Site Monod)

Speaker: Amine Marrakchi

Abstract: Interprétation physique des jeux quantique.


Title: Tsirelson-Connes reading group

Time: Thursday Feb 6th at 10:15

Place: Salle 435, ENS de Lyon (Site Monod)

Speaker: Omar Fawzi and Mikael de la Salle

Abstract: The objective is to read the paper "MIP*=RE" (arXiv:2001.04383). Introduction to Connes embedding problem and Tsirelson problem.


Title: Introduction to representation theory and Schur Weyl duality (Representation Theory of the Symmetric Group)

Time: Thursday Jan 30th at 10am

Place: Salle du conseil du LIP 394 Nord, ENS de Lyon (Site Monod)

Speaker: Aadil Oufkir

Abstract: 


Title: Introduction to representation theory and Schur Weyl duality

Time: Monday Jan 27th at 10:15am

Place: Salle de reunion du M7, ENS de Lyon (Site Monod)

Speaker: Aadil Oufkir

Abstract: We're planning to start a series of introductory lectures on representation theory applied to quantum information. After an introduction, Aadil will try to give parts of the proof of Schur Weyl duality.


Title: On pohyedral approximations of the positive semidefinite cone (part 2)

Time: Jan 21st at 11:30am

Place: Salle du conseil du LIP 394 Nord, ENS de Lyon (Site Monod)

Speaker: Guillaume Aubrun (Lyon 1)

Abstract: We illustrate the fact that Semi Definite Programming is more powerful than Linear Programming by proving the following theorem: any polyhedral cone which approximates the cone of n x n positive matrices has extension complexity at least exp(c sqrt(n)). The proof uses notably the hypercontractivity inequality on the discrete cube. The talk will be self-contained. Reference: https://arxiv.org/abs/1811.09649


Title: On pohyedral approximations of the positive semidefinite cone

Time: Jan 14th at 11:30am

Place: Salle du conseil du LIP 394 Nord, ENS de Lyon (Site Monod)

Speaker: Guillaume Aubrun (Lyon 1)

Abstract: We illustrate the fact that Semi Definite Programming is more powerful than Linear Programming by proving the following theorem: any polyhedral cone which approximates the cone of n x n positive matrices has extension complexity at least exp(c sqrt(n)). The proof uses notably the hypercontractivity inequality on the discrete cube. The talk will be self-contained. Reference: https://arxiv.org/abs/1811.09649


2019:

Title: Sharing nonlocality with a single entangled qubit pair

Time: Dec 10th at 11:30am

Place: Salle du conseil du LIP 394, ENS de Lyon (Site Monod)

Speaker: Peter Brown (LIP, ENS Lyon)

Abstract:

 


Title: Entangleability of cones

Time: Nov 12th at 11:30am

Place: Salle de reunion du M7, ENS de Lyon (Site Monod)

Speaker: Guillaume Aubrun (Lyon 1)

Abstract: Given two convex finite-dimensional cones, one can naturally define their minimal and their maximal tensor product. We show that both coincide exactly when one of the cones is isomorphic to the positive orthant, as was conjectured by Barker (1976). An interpretation is as follows: the phenomenon of entanglement is universal among probabilistic theories which are not classical (quantum mechanics being a particular case).

 


Title: Reznick's Positivstellensatz and applications to quantum information theory

Time: Nov 5th at 11:30am

Place: Salle du conseil du LIP 394 Nord, ENS de Lyon (Site Monod)

Speaker: Alexander Muller-Hermes (Lyon 1)

Abstract: In his solution of Hilbert’s 17th problem Artin showed that any positive definite polynomial in several variables can be written as the quotient of two sums of squares. Later Reznick showed that the denominator in Artin’s result can always be chosen as an N-th power of a specific quadratic form and gave explicit bounds on N. By using concepts from quantum information theory (such as partial traces and an identity due to Chiribella) we present a simpler proof of a complex version of this result and we will mention applications to quantum information theory.

 


Title: Hamiltonian complexity meets derandomization

Time: Oct 15th at 11:30am

Place: Salle de réunion du M7, ENS de Lyon (Site Monod)

Speaker: Alex Grilo (CWI)

Abstract: The derandomization of MA, the probabilistic version of NP, is a long standing open question. In this work, we connect this problem to a variant of another major problem: the quantum PCP conjecture. Our connection goes through the surprising quantum characterization of MA by Bravyi and Terhal. They proved the MA-completeness of the problem of deciding whether the groundenergy of a uniform stoquastic local Hamiltonian is zero or inverse polynomial. We show that the gapped version of this problem, i.e. deciding if a given uniform stoquastic local Hamiltonian is frustration-free or has energy at least some constant ϵ, is in NP. Thus, if there exists a gap-amplification procedure for uniform stoquastic Local Hamiltonians (in analogy to the gap amplification procedure for constraint satisfaction problems in the original PCP theorem), then MA = NP (and vice versa). Furthermore, if this gap amplification procedure exhibits some additional (natural) properties, then P = RP. We feel this work opens up a rich set of new directions to explore, which might lead to progress on both quantum PCP and derandomization. As a small side result, we also show that deciding if commuting stoquastic Hamiltonian is frustration free is in NP.

Joint work with Dorit Aharonov.

 


Title: Exponential Separation between Quantum Communication and Logarithm of Approximate Rank

Time: Oct 8th at 10:15am

Place: Salle du Conseil du LIP 394, ENS de Lyon (Site Monod)

Speaker: Makrand Sinha (CWI)

Abstract: Chattopadhyay, Mande and Sherif (to appear in STOC 2019) recently exhibited a total Boolean function, the sink function, that has polynomial approximate rank and polynomial randomized communication complexity. This gives an exponential separation between randomized communication complexity and logarithm of the approximate rank, refuting the log-approximate-rank conjecture. We show that even the quantum communication complexity of the sink function is polynomial, thus also refuting the quantum log-approximate-rank conjecture. Our lower bound is based on the fooling distribution method introduced by Rao and Sinha (Theory of Computing 2018) for the classical case and extended by Anshu, Touchette, Yao and Yu (STOC 2017) for the quantum case. We also give a new proof of the classical lower bound using the fooling distribution method.

Joint work with Ronald de Wolf.