Small sets of locally indistinguishable orthogonal maximally entangled states

Abstract

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 $k\le d$ orthogonal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ 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.

8 pages, single column, published version

References in corpus (4)

• A framework for bounding nonlocality of state discrimination
• PPT-indistinguishable states via semidefinite programming
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Tight bounds on the distinguishability of quantum states under separable measurements

Cited by in corpus (1)

• Quantum Error Correction and One-Way LOCC State Distinguishability