2013/07/31 by Alessandro Cosentino, Vincent Russo
Physics and Astronomy · #quant-ph
published as Quantum Information & Computation, Vol.14 No.13&14, 1098--1106 (2014) · 8 pages, single column, published version
arxiv created 2014/08/21 · arxiv updated 2014/08/22
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) -- arXiv:1107.3224 [quant-ph]] 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.