Full Bell locality of a noisy state for $N\geq 3$ nonlocally entangled qudits

TL;DR

This paper derives new bounds on the full Bell locality of noisy N-qudit states, extending beyond known separability limits, by analyzing maximal Bell inequality violations using dilation characteristics.

Contribution

It introduces analytical upper bounds on Bell locality for noisy N-qudit states based on dilation properties, applicable for all dimensions and qudit numbers.

Findings

New bounds on Bell locality surpass known separability limits.

Bounds are valid for all d ≥ 2 and N ≥ 3.

Applicable to GHZ and arbitrary N-qudit states with white noise.

Abstract

Bounds, expressed in terms of d and N, on full Bell locality of a quantum state for $N\geq 3$ nonlocally entangled qudits (of a dimension $d\geq 2$) mixed with white noise are known, to our knowledge, only within full separability of this noisy N-qudit state. For the maximal violation of general Bell inequalities by an N-partite quantum state, we specify the analytical upper bound expressed in terms of dilation characteristics of this state, and this allows us to find new general bounds in $d, N$, valid for all $d\geq 2$ and all $N\geq 3$, on full Bell locality under generalized quantum measurements of (i) the N-qudit GHZ state mixed with white noise and (ii) an arbitrary N-qudit state mixed with white noise. The new full Bell locality bounds are beyond the known ranges for full separability of these noisy N-qudit states.