What is the minimum CHSH score certifying that a state resembles the singlet?

TL;DR

This paper investigates the minimum CHSH violation needed to certify that a quantum state is close to a singlet, providing a new analytical approach in a device-independent setting and showing a higher threshold than previously known.

Contribution

It introduces a novel analytical method to determine the minimal CHSH violation for certifying singlet-like states in a device-independent framework, raising the threshold from about 2.0014 to 2.05.

Findings

Minimum CHSH violation for non-trivial fidelity is approximately 2.05.

Device-independent bounds differ significantly from device-dependent cases.

New analytical approach broadens understanding of Bell inequality violations and state certification.

Abstract

A quantum state can be characterized from the violation of a Bell inequality. The well-known CHSH inequality for example can be used to quantify the fidelity (up to local isometries) of the measured state with respect to the singlet state. In this work, we look for the minimum CHSH violation leading to a non-trivial fidelity. In particular, we provide a new analytical approach to explore this problem in a device-independent framework, where the fidelity bound holds without assumption about the internal working of devices used in the CHSH test. We give an example which pushes the minimum CHSH threshold from $\approx2.0014$ to $\approx2.05,$ far from the local bound. This is in sharp contrast with the device-dependent (two-qubit) case, where entanglement is one-to-one related to a non-trivial singlet fidelity. We discuss this result in a broad context including device-dependent/independent state characterizations with various classical resources.