New Quantum Bounds for Inequalities involving Marginal Expectations

TL;DR

This paper develops an algorithm to determine quantum bounds for inequalities involving marginal expectations, deriving new bounds and analyzing the quantum volume, thereby advancing understanding of quantum correlations beyond previous models.

Contribution

The paper introduces a novel algorithm for calculating quantum bounds, deriving new number-valued and function-valued bounds, and extending quantum volume analysis.

Findings

Derived new quantum bounds including function-valued bounds

Extended quantum volume analysis to 8 dimensions

Proved the new bounds are more complete than existing hierarchical inequalities

Abstract

We review, correct, and develop an algorithm which determines arbitrary Quantum Bounds, based on the seminal work of Tsirelson [Lett. Math. Phys. 4, 93 (1980)]. The potential of this algorithm is demonstrated by deriving both new number-valued Quantum Bounds, as well as identifying a new class of function-valued Quantum Bounds. Those results facilitate an 8-dimensional Volume Analysis of Quantum Mechanics which extends the work of Cabello [PRA 72 (2005)]. We contrast the Quantum Volume defined be these new bounds to that of Macroscopic Locality, defined by the inequalities corresponding to the first level of the hierarchy of Navascues et al [NJP 10 (2008)], proving our function-valued Quantum Bounds to be more complete.