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

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 $\approx 2.0014$ to $\approx 2.05,$ 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.

arXiv comment15 pages (7+8), 2 figures

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Cited by in corpus (8)

• Noisy pre-processing facilitating a photonic realisation of device-independent quantum key distribution
• Semidefinite programming relaxations for quantum correlations
• Device-independent quantum key distribution from generalized CHSH inequalities
• Self-testing with finite statistics enabling the certification of a quantum network link
• Self-testing two-qubit maximally entangled states from generalized CHSH tests
• Bounding conditional entropy of bipartite states with Bell operators
• Composable framework for device-independent state certification
• Comparing Singlet Testing Schemes