Small sets of locally indistinguishable orthogonal maximally entangled
states
(pp1098-1106)
Alessandro
Cosentino and Vincent Russo
doi:
https://doi.org/10.26421/QIC14.13-14-3
Abstracts:
We study the problem of distinguishing quantum states
using local operations and classical communication (LOCC). A question of
fundamental interest is whether there exist sets of k ≤ d orthogonal
maximally entangled states in Cd ⊗ Cd that are not perfectly
distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys.
Rev. Lett. 109 020506 (2012)] gives an affirmative answer for the case k
= d. We give, for the first time, a proof that such sets of states
indeed exist even in the case k < d. Our result is constructive and
holds for an even wider class of operations known as
positive-partial-transpose measurements (PPT). The proof uses the
characterization of the PPT-distinguishability problem as a semidefinite
program.
Key words:
LOCC, PPT, state distinguishability, semidefinite programming |