Distinguishing generic quantum states
Seminar author:Karol Życskowski
Event date and time:09/19/2017 02:30:pm
Event location:GIQ Seminar Room
Event contact:michail.skoteiniotis@uab.cat
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
$1/4+1/\pi$, 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. Asymptotic value for the root fidelity between two random states,
$\sqrt{F}=3/4$, can serve as a universal reference value
for further theoretical and experimental studies.
Analogous results for quantum relative entropy and
Chernoff quantity provide other bounds on the distinguishablity of both states
in a multiple measurement setup due to the quantum Sanov theorem. Entanglement
of a generic mixed state of a bi–partite system is estimated.