Violation of general Bell inequalities by a pure bipartite quantum state

TL;DR

This paper derives a new upper bound on the maximal violation of general Bell inequalities for pure bipartite quantum states, showing limitations on quantum nonlocality in infinite-dimensional systems with specific state structures.

Contribution

It introduces a novel upper bound on Bell inequality violations for infinite-dimensional pure bipartite states, extending previous formalism and applying it to coherent states.

Findings

Violation bounded by 3 for certain bipartite coherent states

Upper bounds are independent of measurement settings and outcomes

Numerical analysis of bounds' dependence on state parameters

Abstract

In the present article, based on the formalism introduced in [Loubenets, J. Math. Phys. 53, 022201 (2012)], we derive for a pure bipartite quantum state a new upper bound on its maximal violation of general Bell inequalities. This new bound indicates that, for an infinite dimensional pure bipartite state with a finite sum of its Schmidt coefficients, violation of any general Bell inequality is bounded from above by the value independent on a number of settings and a type of outcomes, continuous or discrete, specific to this Bell inequality. As an example, we apply our new general results to specifying upper bounds on the maximal violation of general Bell inequalities by infinite dimensional bipartite states having the Bell states like forms comprised of two binary coherent states $|\alpha\rangle ,|-\alpha\rangle$, with $\alpha>0$. We show that, for each of these bipartite coherent states, the maximal violation of general Bell inequalities cannot exceed the value $3$ and analyse numerically the dependence of the derived analytical upper bounds on a parameter $\alpha>0$.