LOCC distinguishable orthogonal product states with least entanglement resource

Abstract

In this paper, we construct $2n-1$ locally indistinguishable orthogonal product states in ${\mathbb{C}}^n\otimes {\mathbb{C}}^4(n>4)$ and ${\mathbb{C}}^n\otimes {\mathbb{C}}^5(n\ge 5)$ respectively. Moreover, a set of locally indistinguishable orthogonal product states with $2(n+2l)-8$ elements in ${\mathbb{C}}^n\otimes {\mathbb{C}}^{2l}(n\ge 2l>4)$ and a class of locally indistinguishable orthogonal product states with $2(n+2k+1)-7$ elements in ${\mathbb{C}}^n\otimes {\mathbb{C}}^{2k+1}(n\ge 2k+1>5)$ are also constructed respectively. These classes of quantum states are then shown to be distinguishable by local operation and classical communication (LOCC) using a suitable ${\mathbb{C}}^2\otimes {\mathbb{C}}^2$ maximally entangled state respectively.

arXiv comment10 pages, 3 figures

References in corpus (18)

• Quantum Cryptography
• Quantum Nonlocality without Entanglement
• Quantum Teleportation with a Complete Bell State Measurement
• Multi-step quantum secure direct communication using multi-particle Green-Horne-Zeilinger state
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability and LOCC monotones
• Local indistinguishability: more nonlocality with less entanglement
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Nonlocality of orthogonal product basis quantum states
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local distinguishability with preservation of entanglement
• Local indistinguishability of orthogonal product states
• Three maximally entangled states can require two-way LOCC for local discrimination
• Any $2\otimes n$ subspace is locally distinguishable
• Local Distinguishability of Any Three Quantum States

Cited by in corpus (2)

• Locality of Orthogonal Product States via Multiplied Copies
• The Independence of Distinguishability and the Dimension of the System