All-versus-nothing proofs with n qubits distributed between m parties

TL;DR

This paper presents a method to determine if an n-qubit distributed state among m parties admits an all-versus-nothing proof using only single-qubit measurements, and classifies such proofs for small systems.

Contribution

It introduces a novel method to identify AVN proofs in distributed quantum states and provides a complete classification for systems with fewer than nine qubits.

Findings

Method to decide AVN proofs for distributed states

All inequivalent AVN proofs with less than nine qubits

Classification of minimal AVN proofs for small systems

Abstract

All-versus-nothing (AVN) proofs show the conflict between Einstein, Podolsky, and Rosen's elements of reality and the perfect correlations of some quantum states. Given an n-qubit state distributed between m parties, we provide a method with which to decide whether this distribution allows an m-partite AVN proof specific for this state using only single-qubit measurements. We apply this method to some recently obtained n-qubit m-particle states. In addition, we provide all inequivalent AVN proofs with less than nine qubits and a minimum number of parties.