Exploring strong locality : Quantum state discrimination regime and beyond

TL;DR

This paper investigates the nuanced interplay of locality and nonlocality in quantum state discrimination, introducing new classes of distinguishable sets, exploring their applications in data hiding, and defining the concept of 'strong local' sets.

Contribution

It presents two new classes of locally distinguishable quantum states, analyzes their nonlocality properties, and introduces the concept of 'strong local' sets, advancing understanding of quantum locality phenomena.

Findings

One class exhibits nonlocality via local operations.

Another class requires joint measurements to reveal nonlocality.

The study highlights differences in locality levels among quantum state sets.

Abstract

Based on the conviction of switching information from locally accessible to locally hidden environs, the concept of hidden nonlocality activation has recently been highlighted by Bandyopadhyay et al. in [Phys. Rev. A 104, L050201 (2021)]. They have demonstrated that a certain locally distinguishable set of pure quantum states can be transformed into a locally indistinguishable set with certainty through orthogonality preserving local measurements (OPLMs). This transformation makes the set locally inaccessible, despite being locally accessible before. This phenomenon is defined as the activation of hidden nonlocality. In this paper, we present two classes of locally distinguishable sets within $(2m+1) \otimes 2 \otimes (2m+1)$ systems. One class reveals nonlocality through local operations, whereas the other requires joint measurements for it. As the later class depends on nonlocal operations to exhibit nonlocality, it arguably has a lower degree of nonlocality, and accordingly, can be considered as more local compared to the first class. This analysis exhibits a stronger manifestation of locality by elucidating the nuanced interplay between these distinct local phenomena within the framework of quantum state discrimination. Furthermore, we also explore their significant applications in the context of data hiding. Additionally, we introduce the concept of \emph{``strong local"} set and compare it with various activatable sets, highlighting differences in terms of locality.