Nonlocality without entanglement: Party asymmetric case

Abstract

A set of orthogonal product states of a composite Hilbert space is genuinely nonlocal if the states are locally indistinguishable across any bipartition. In this work, we construct a minimal set of party asymmetry genuine nonlocal set in arbitrary large dimensional composite quantum systems $C^d\otimes C^d\otimes C^d$. We provide a local discriminating protocol by using a three qubit GHZ state as a resource. On the contrary, we observe that single-copy of two qubit Bell states provide no advantage for this discrimination task. Recently, Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)], proposed the concept of strong nonlocality without entanglement and ask an open question whether there exist an incomplete strong nonlocal set or not. In [Phys. Rev. A 102, 042228 (2020)], an answer is provided by the authors. Here, we construct an incomplete party asymmetry strong nonlocal set which is more stronger than the set constructed in [Phys. Rev. A 102, 042228 (2020)] with respect to the consumption of entanglement as a resource for their respective discrimination tasks.

17 pages, 2 figures, revtex, comments welcome

References in corpus (4)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)

Cited by in corpus (7)

• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• More assistance of entanglement, less rounds of classical communication
• Exploring strong locality : Quantum state discrimination regime and beyond
• Classifying locally distinguishable sets: No activation across bipartitions
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Multipartite Monogamy of Entanglement for Three Qubit States
• Entanglement of Assistance as a measure of multiparty entanglement