Self-guided method to search maximal Bell violations for unknown quantum states
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Abstract
In recent decades, a great variety of research 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-guided method to find MBVs for unknown states using a stochastic gradient ascent algorithm (SGA), by parametrizing the corresponding Bell operators. For three investigated systems (two qubit, three qubit, and two qutrit), this method can ascertain the MBV of general two-setting inequalities within 100 iterations. Furthermore, we prove SGA is also feasible when facing more complex Bell scenarios, e.g., $d$-setting $d$-outcome Bell inequality. Moreover, compared to other possible methods, SGA exhibits significant superiority in efficiency, robustness, and versatility.