Semi-device-independent bounds on entanglement

TL;DR

This paper introduces Bell-type inequalities that enable semi-device-independent bounds on entanglement, specifically concurrence, in two-qubit systems, without detailed measurement knowledge, relying only on Hilbert space dimension assumptions.

Contribution

It develops a family of Bell inequalities that provide bounds on entanglement measures in a semi-device-independent framework, expanding tools for entanglement verification.

Findings

Derived explicit bounds on concurrence for two-qubit states.

Established that these bounds can be obtained with minimal measurement assumptions.

Demonstrated the inequalities cannot be maximally violated by finite-dimensional maximally entangled states.

Abstract

Detection and quantification of entanglement in quantum resources are two key steps in the implementation of various quantum-information processing tasks. Here, we show that Bell-type inequalities are not only useful in verifying the presence of entanglement but can also be used to bound the entanglement of the underlying physical system. Our main tool consists of a family of Clauser-Horne-like Bell inequalities that cannot be violated maximally by any finite-dimensional maximally entangled state. Using these inequalities, we demonstrate the explicit construction of both lower and upper bounds on the concurrence for two-qubit states. The fact that these bounds arise from Bell-type inequalities also allows them to be obtained in a semi-device-independent manner, that is, with assumption of the dimension of the Hilbert space but without resorting to any knowledge of the actual measurements being performed on the individual subsystems.