Stoquastic permutationally invariant Bell operators

TL;DR

This paper investigates the relationship between permutationally invariant Bell operators and stoquasticity, introducing a new framework to characterize and optimize their properties, with implications for quantum nonlocality experiments.

Contribution

It establishes the first connection between PI Bell operators and stoquasticity, introducing the stoquasticity cone for full characterization and optimization.

Findings

PI Bell operators with up to three-body correlators can always be made stoquastic.

The largest Bell-correlation experiments use operators close to optimal in stoquasticity.

The work provides a new tool for optimizing quantum-classical gaps in Bell tests.

Abstract

As Hermitian operators, many-body Bell operators can naturally be identified as many-body Hamiltonians. An important subclass of such Hamiltonians is the stoquastic class, characterized by having nonpositive off-diagonal matrix elements in a given basis. Interestingly, this property is shared by the permutationally invariant (PI) Bell operators underlying the largest Bell-correlation experiments to date. In this work, we explore the connection between many-body PI Bell operators and stoquasticity. We introduce the stoquasticity cone, which allows for a full characterization of the stoquastic parameter regimes for any PI Bell operator. We use this to show that PI Bell operators of the binary-input binary-output scenario consisting of at most three-body correlators can always be rendered stoquastic for any set of measurement parameters. Additionally, we also provide examples that use the stoquasticity cone to optimize for the quantum-classical gap. Numerical evidence suggests that the Bell operator used in the largest experiments to date is optimal with respect to stoquasticity. To the best of our knowledge, this work establishes the first connection between PI Bell operators and stoquasticity.