Distinguishability of Quantum States by Separable Operations

Abstract

Abstract- (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.

Any2⊗nsubspace is locally distinguishable

“…We show that any 2 ⊗ n subspace is locally distinguishable. Combining with the previous results [4,12,13], we conclude that there is no locally indistinguishable m ⊗ n subspace if and only if m 2 or n 2. Our key techniques can be used to study the distinguishability of three-dimensional bipartite subspace which contains a product state.…”

“…Watrous also proved that there is no 2 ⊗ 2 locally indistinguishable subspace, by directly employing the results from [11]. Winter's result [5] implies that the existence of bipartite subspace Q such that Q ⊗k is locally indistinguishable for any k. Duan et al generalized Watrous's result to the most general m ⊗ n systems for m = n and the multipartite setting, and found locally indistinguishable subspaces with smaller dimensions [12,13]. Most notably, it was shown that any subspace spanned by three-qubit UPB is locally indistinguishable, and there exists a three-dimensional * nengkunyu@gmail.com † runyao.duan@uts.edu.au ‡ mying@it.uts.edu.au three-qubit locally indistinguishable subspace [13].…”

Limitations on Separable Measurements by Convex Optimization

“…This resolves an open question raised in [DFXY09]. We also show that every unextendable product set together with one extra pure state orthogonal to every member of the unextendable product set is not perfectly discriminated by separable measurements.…”

Realizing a 2-D Positive Operator-Valued Measure by Local Operations and Classical Communication

“…According to Naimark's theorem, any non-projective measurement can be realized by a projective measurement on an extended Hilbert space. However, if a 2D non-projective measurement has more than two POVM operators, then so does the corresponding projective measurement, and such a measurement often cannot be realized by LOCC [16][17][18]. Thus, this approach cannot directly answer the question.…”