Small sets of genuinely nonlocal GHZ states in multipartite systems

TL;DR

This paper constructs small sets of generalized GHZ states that are genuinely nonlocal in multipartite systems, revealing minimal configurations that exhibit nonlocality across all bipartitions and highlighting limitations of existing detection methods.

Contribution

It introduces methods to identify tiny genuinely nonlocal sets of GHZ states in large multipartite systems, advancing understanding of quantum nonlocality with minimal state sets.

Findings

A small proportion of GHZ basis states exhibit genuine nonlocality in large N-qubit systems.

Existence of d+1 genuinely nonlocal GHZ states in systems with large local dimension d.

Limitations of TOPLM technique in detecting genuine nonlocality are demonstrated.

Abstract

A set of orthogonal multipartite quantum states are called (distinguishability-based) genuinely nonlocal if they are locally indistinguishable across any bipartition of the subsystems. In this work, we consider the problem of constructing small genuinely nonlocal sets consisting of generalized GHZ states in multipartite systems. For system (C^2)^(\otimes N) where N is large, using the language of group theory, we show that a tiny proportion {\Theta}[1/2^(N/2)] of the states among the N-qubit GHZ basis suffice to exhibit genuine nonlocality. Similar arguments also hold for the canonical generalized GHZ bases in systems (C^d)^(\otimes N), wherever d is even and N is large. What is more, moving to the condition that any fixed N is given, we show that d + 1 genuinely nonlocal generalized GHZ states exist in (C^d)^(\otimes N), provided the local dimension d is sufficiently large. As an additional merit, within and beyond an asymptotic sense, the latter result also indicates some evident limitations of the "trivial othogonality-preserving local measurements" (TOPLM) technique that has been utilized frequently for detecting genuine nonlocality.