Distinguishability of Quantum States by Separable Operations

TL;DR

This paper characterizes when multipartite quantum states can be distinguished by separable operations, revealing new classes of nonlocal operations and constructing smaller indistinguishable subspaces, advancing understanding of quantum state discrimination.

Contribution

It provides a necessary and sufficient condition for distinguishability by separable operations and constructs smaller indistinguishable subspaces, extending previous results.

Findings

Existence of 2x2 separable operations not realizable by LOCC

Explicit construction of smaller indistinguishable subspaces of dimensions 6 and 7

Generalization of indistinguishability criteria to multipartite states

Abstract

We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of $(D-1)$ pure states, where $D$ is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of $2\otimes 2$ separable operations not being realizable by local operations and classical communication. Before our work only a class of $3\otimes 3$ nonlocal separable operations was known [Bennett et al, Phys. Rev. A \textbf{59}, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of 1 or 2 orthogonal product states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. \textbf{95}, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.