Non-locality and entanglement in multi-qubit systems from a unified framework

TL;DR

This paper demonstrates that violations of nonlocality and entanglement inequalities in multi-qubit systems can be understood as violations of classical probability rules, using a unified framework based on negative probabilities.

Contribution

It introduces a unified approach showing that all nonlocality and entanglement violations stem from classical probability rule violations, without relying on underlying theories.

Findings

Violation of any nonlocality inequality implies negative probabilities.

Entanglement witnesses can be derived as violations of classical probability rules.

Provides a complementary perspective to algebraic approaches.

Abstract

Non-classical probability is the underlying feature of quantum mechanics. The emergence of Bell-CHSH non-locality for bipartite systems and linear entanglement inequalities for two-qubit systems has been shown in Adhikary et al. 2020 [Eur. Phys. J. D 74, 68 (2020)], purely as violations of classical probability rules. In this paper, we improve upon that work by showing that violation of any nonlocality inequality implies violation of classical probability rules, manifested through negative probabilities, without recourse to any underlying theory. Moving on to entanglement, we employ parent pseudoprojections to show how any number of linear and nonlinear entanglement witnesses for multiqubit systems can be obtained as violations of classical probability rules. They include the ones that have been derived earlier by employing different methods. It provides a perspective complementary to the current understanding in terms of the algebraic approaches.