Friday, July 12, 2013

1307.3232 (Alessandro Cosentino et al.)

Small sets of locally indistinguishable orthogonal maximally entangled

Alessandro Cosentino, Vincent Russo
We show how to construct sets of fewer than $d$ orthogonal maximally entangled states in $C^d \otimes C^{d}$ that are not perfectly distinguishable by local operations and classical communication (LOCC). This improves upon previous results, which only showed sets of $k \geq d$ such states. Our results hold for an even wider class of operations, which is the class of positive-partial-transpose measurements (PPT). The proof uses the characterization of the PPT distinguishability problem as a semidefinite program. As an explicit example, we exhibit a set of 15 locally indistinguishable maximally entangled states in $C^{16} \otimes C^{16}$.
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