ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Linear Algebra and Quantum Computation

Wed 11:30–12:00, Auditorium Jean Monnet
Continuity of many-party correlations
Stephan Weis (Unicamp)
Joint work with Leiba Rodman (College of William and Mary); Ilya M. Spitkovsky (College of William and Mary); Arleta Szkola (Max Planck Institute for Mathematics in the Sciences); Konrad Szymanski (Jagiellonian University); Karol Zyczkowski (Jagiellonian University)

This talk is about a measure $c_k$ of quantum many-party correlations, defined as the missing von Neumann entropy which a state has less than the maximum-entropy state compatible with all its marginals on subsystems composed of k parties. The measure $c_k$ is a sum of irreducible correlations defined by Linden et al. 2002 and Zhou 2008.

While $c_k$ is continuous in probability theory (commutative algebra of observables), the measure $c_2$ is discontinuous for three qubits because the maximum-entropy inference is discontinuous (SW/Knauf 2012). We mention some results and open problems about the continuity, including recent work by Rodman/Spitkovsky/Szkola/SW, JMP '16, and by SW, Spitkovsky/SW, and Szymanski/SW/Zyczkowski.