A self-guide method to search maximal Bell violation for unknown quantum states

TL;DR

This paper introduces a self-guided stochastic gradient ascent method to efficiently find the maximal Bell violation for unknown quantum states, improving accuracy and robustness in quantum nonlocality experiments.

Contribution

A novel self-guide method using stochastic gradient ascent for determining maximal Bell violations in unknown quantum states, applicable to various quantum systems.

Findings

Accurately finds MBV within 100 iterations for 2-qubit, 3-qubit, and 2-qutrit systems.

Outperforms other methods in efficiency, robustness, and versatility.

Applicable to Bell experiments involving unknown quantum states.

Abstract

In recent decades, a great variety of researches and applications concerning Bell nonlocality have been developed with the advent of quantum information science. Providing that Bell nonlocality can be revealed by the violation of a family of Bell inequalities, finding maximal Bell violation (MBV) for unknown quantum states becomes an important and inevitable task during Bell experiments. In this paper we introduce a self-guide method to find MBVs for unknown states using a stochastic gradient ascent algorithm (SGA), by parameterizing the corresponding Bell operators. For all the investigated systems (2-qubit, 3-qubit and 2-qutrit), this method can ascertain the MBV accurately within 100 iterations. Moreover, SGA exhibits significant superiority in efficiency, robustness and versatility compared to other possible methods.