Graph connectivity based strong quantum nonlocality with genuine entanglement

Abstract

Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to be of strong nonlocality if it is locally irreducible for every bipartition of the subsystems. Most of the known results are limited to sets with product states. Shi et al. presented the first result of strongly nonlocal entangled sets in [Phys. Rev. A 102, 042202 (2020)] and there they questioned the existence of strongly nonlocal set with genuine entanglement. In this work, we relate the strong nonlocality of some speical set of genuine entanglement to the connectivities of some graphs. Using this relation, we successfully construct sets of genuinely entangled states with strong nonlocality. As a consequence, our constructions give a negative answer to Shi et al.'s question, which also provide another answer to the open problem raised by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. This work associates a physical quantity named strong nonlocality with a mathematical quantity called graph connectivity.

arXiv comment8 Pages, 5 figures, a small modification of Fig.2 and Fig.3

References in corpus (40)

• Quantum Nonlocality without Entanglement
• Unextendible Product Bases and Bound Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Graph States for Quantum Secret Sharing
• Quantum Data Hiding
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Hiding bits in Bell states
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability and LOCC monotones
• Local indistinguishability: more nonlocality with less entanglement
• Maximally multipartite entangled states
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Genuinely multipartite entangled states and orthogonal arrays
• Strong Quantum Nonlocality without Entanglement
• Quantum secret sharing based on local distinguishability
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Nonlocality of orthogonal product basis quantum states
• Distinguishability of complete and unextendible product bases
• Local distinguishability with preservation of entanglement
• Several nonlocal sets of multipartite pure orthogonal product states
• LOCC distinguishability of unilaterally transformable quantum states
• Local indistinguishability of orthogonal product states
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Exploring pure quantum states with maximally mixed reductions
• PPT-indistinguishable states via semidefinite programming
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Strong Quantum Nonlocality without Entanglement in Multipartite Quantum Systems
• Strong quantum nonlocality with entanglement
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Constructing locally indistinguishable orthogonal product bases in an $m\otimes n$ system
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Locally distinguishing quantum states with limited classical communication
• Twist-teleportation based local discrimination of maximally entangled states
• Alternative method for deriving nonlocal multipartite product states
• Positive-partial-transpose distinguishability for lattice-type maximally entangled states