Characterizing locally indistinguishable orthogonal product states

Bennett et al. Physical Review A, vol. 59, no. 2, p. 1070, 1999] identified a set of orthogonal product states in the Hilbert space ℂ3 ⊗ ℂ3 such that reliably distinguishing those states requires nonlocal quantum operations. While more examples have been found for this counterintuitive "nonlocality without entanglement" phenomenon, a complete and computationally verifiable characterization for all such sets of states remains unknown. In this paper, we give such a characterization for both ℂ3 ⊗ ℂ3 and ℂ2 ⊗ ℂ2 ⊗ ℂ2. As a consequence, we show that in both spaces, there is no additional set of a fundamentally different structure than those of the known instances. © 2009 IEEE

Nonlocality, Asymmetry, and Distinguishing Bipartite States

Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of 2x2 quantum states to be locally distinguishable, and for a general set of 2xn quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of ``nonlocality without entanglement'', and we present a very simple proof of this phenomenon.Comment: 5 pages, 1 figure. Improved in line with referees comments, references added, typo corrected. To appear in Phys. Rev. Let

The Structure of Qubit Unextendible Product Bases

Unextendible product bases have been shown to have many important uses in quantum information theory, particularly in the qubit case. However, very little is known about their mathematical structure beyond three qubits. We present several new results about qubit unextendible product bases, including a complete characterization of all four-qubit unextendible product bases, which we show there are exactly 1446 of. We also show that there exist p-qubit UPBs of almost all sizes less than $2^p$.Comment: 20 pages, 3 tables, 7 figure

Three maximally entangled states can require two-way LOCC for local discrimination

We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$-dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.Comment: 23 pages, 1 figure, 1 table. (Published version