Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$

Abstract

A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. Although such a phenomenon has been shown to any three-, four-, and five-partite systems, the existence of strongly nonlocal orthogonal product sets in multipartite systems remains unknown. In this paper, by using a general decomposition of the $N$-dimensional hypercubes, we present strongly nonlocal orthogonal product sets in $N$-partite systems for all odd $N\ge 3$. Based on this decomposition, we give explicit constructions of unextendible product bases in $N$-partite systems for odd $N\ge 3$. Furthermore, we apply our results to quantum secret sharing, uncompletable product bases, and PPT entangled states.

arXiv comment24 pages, 2 figures

References in corpus (45)

• Quantum entanglement
• Bell nonlocality
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• 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
• Multipartite Nonlocality without Entanglement in Many Dimensions
• Distinguishability of the Bell states
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability: more nonlocality with less entanglement
• Local indistinguishability and LOCC monotones
• Strong Quantum Nonlocality without Entanglement
• Distinguishability of maximally entangled states
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Nonlocality of orthogonal product basis quantum states
• Distinguishability of complete and unextendible product bases
• Several nonlocal sets of multipartite pure orthogonal product states
• Local indistinguishability of orthogonal product states
• PPT-indistinguishable states via semidefinite programming
• Strong Quantum Nonlocality without Entanglement in Multipartite Quantum Systems
• Strong quantum nonlocality with entanglement
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• Bell inequalities with no quantum violation and unextendible product bases
• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• Tight Bell inequalities with no quantum violation from qubit unextendible product bases
• Entanglement, mixedness and perfect local discrimination of orthogonal quantum states
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Nonlocality without entanglement in general multipartite quantum systems
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• Local distinguishability based genuinely quantum nonlocality without entanglement
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Locally stable sets with minimum cardinality
• Unextendible Product Basis for Fermionic Systems
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Unextendible and uncompletable product bases in every bipartition
• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
• Small set of orthogonal product states with nonlocality
• Strong quantum nonlocality from hypercubes
• Positive-partial-transpose distinguishability for lattice-type maximally entangled states
• On the state space structure of tripartite quantum systems
• Genuinely nonlocal sets with smallest cardinality

Cited by in corpus (6)

• Genuinely nonlocal sets without entanglement in multipartite systems
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Strongest quantum nonlocality in $N$-partite systems
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Progress in the study of the (non)existence of genuinely unextendible product bases