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
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.