Upper bounds on violation of Bell-type inequalities by a multipartite quantum state

TL;DR

This paper derives exact upper bounds on the maximum violation of Bell-type inequalities for various multipartite quantum states, regardless of the system's dimension, with implications for quantum nonlocality limits.

Contribution

It provides the first precise upper bounds on Bell violations applicable to arbitrary N-partite states, including infinite-dimensional systems.

Findings

Violation bounds scale as (2S-1)^{N-1} for any N-partite state.

Bounds are valid for any number of measurement settings and outcomes.

Results unify and extend previous bounds for finite and infinite-dimensional systems.

Abstract

We present the new exact upper bounds on the maximal Bell violation for the generalized N-qubit GHZ state, the N-qudit GHZ state and, in general, for an arbitrary N-partite quantum state, possibly infinite-dimensional. Our results indicate that, for an N-partite quantum state of any Hilbert space dimension, violation of any Bell-type inequality (either on correlation functions or on joint probabilities) with S settings and any number of outcomes at each site cannot exceed (2S-1)^{N-1}.