Distinguishing generic quantum states

Seminar date and time: 
Tuesday, 19 September, 2017 - 14:30
Jagiellonian University, Cracow, Poland
Karol Życskowski
GIQ Seminar Room

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.

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