Nonlocality without entanglement: Party asymmetric case

TL;DR

This paper constructs minimal, party asymmetric genuinely nonlocal sets in high-dimensional quantum systems and demonstrates their discrimination using a GHZ state, revealing new insights into nonlocality without entanglement.

Contribution

It introduces a minimal party asymmetric nonlocal set in large dimensions and shows its discrimination protocol using a GHZ state, advancing understanding of nonlocality without entanglement.

Findings

Constructed a minimal party asymmetric nonlocal set in $C^d\otimes C^d\otimes C^d$.

Provided a local discrimination protocol using a GHZ state.

Created an incomplete strong nonlocal set more resource-efficient than previous sets.

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.