Nonlocality without entanglement in general multipartite quantum systems

Abstract

The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $({\mathbb{C}}^d{)}^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon of nonlocality without entanglement more efficiently.

6 pages, 4 figures

References in corpus (5)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Local distinguishability with preservation of entanglement
• Strong quantum nonlocality with entanglement
• Local distinguishability of orthogonal 2\otimes3 pure states
• Detecting the local indistinguishability of maximally entangled states

Cited by in corpus (8)

• Locally stable sets with minimum cardinality
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Strongest nonlocal sets with minimum cardinality in tripartite systems
• Genuinely nonlocal sets without entanglement in multipartite systems
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Unextendible and strongly uncompletable product bases
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries