Locality of Orthogonal Product States via Multiplied Copies

Abstract

In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyze orthogonal product states in any system to show that with LOCC protocols, to distinguish seven orthogonal product states, one can exclude four states via a single copy. In bipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $\lceil \frac{N}{4}\rceil$ copies are allowed, where $\lceil l\rceil$ for a real number $l$ means the smallest integer not less than $l$. In multipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $\lceil \frac{N}{4}\rceil +1$ copies are allowed. We also give a theorem to show how many states can be excluded via a single copy if we are distinguishing n orthogonal product states by LOCC protocols in a bipartite system. Not like previous results, our result is a general result for any set of orthogonal product states in any system.

arXiv comment14 pages, 5 graphs, 7 tables

References in corpus (29)

• Quantum Nonlocality without Entanglement
• Unextendible Product Bases and Bound Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Distinguishability and indistinguishability by LOCC
• Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Distinguishability of maximally entangled states
• Nonlocality of orthogonal product basis quantum states
• Distinguishability of complete and unextendible product bases
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local indistinguishability of orthogonal product states
• Condition for unambiguous state discrimination with local operations and classical communication
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Three maximally entangled states can require two-way LOCC for local discrimination
• More nonlocality with less purity
• Entanglement as a resource for local state discrimination in multipartite systems
• Distinguishing a set of full product bases needs only projective measurements and classical communication
• When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?
• Local Distinguishability of Any Three Quantum States
• Orthogonality And Distinguishability: Criterion For Local Distinguishability of Arbitrary Orthogonal States
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
• Locally distinguishing quantum states with limited classical communication
• Unambiguous discrimination of special sets of multipartite states using local measurements and classical communication
• Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource
• Framework for distinguishability of orthogonal bipartite states by one-way local operations and classical communication
• Local distinguishability of quantum states in multipartite System
• LOCC distinguishable orthogonal product states with least entanglement resource
• Local Distinguishability and Schmidt Number of Orthogonal States

Cited by in corpus (1)

• Application of Ramsey theory to localization of set of product states via multicopies