Probabilistic Operator Algebra Seminar: Phase transitions for random quantum states

Seminar | February 25 | 2-4 p.m. | 736 Evans Hall

 Stanislaw J. Szarek, Case Western Reserve University and Sorbonne University Paris

 Department of Mathematics

Consider a quantum system consisting of N particles, and assume that it is in a random pure state (i.e., uniform over the sphere of the corresponding Hilbert space H). Let A and B be two subsystems consisting of k particles each. Then there exists a threshold value $k_0 \sim N/5$ such that

(i) if $k > k_0$, then A and B typically share entanglement

(ii) if $k < k_0$, then A and B typically do not share entanglement.

We give precise statements of results of the above type and outline the arguments which involve random matrices, majorization, and various concepts/techniques from geometric functional analysis.