Measurement-device-independent quantification of entanglement for given Hilbert space dimension

TL;DR

This paper develops a measurement-device-independent method to quantify entanglement and assess quantum key distribution security based solely on observed correlations and known Hilbert space dimensions, reducing assumptions.

Contribution

It introduces a technique to certify entanglement and security without assuming measurement details, applicable to qubit systems with imperfect detectors.

Findings

Entanglement can be certified with fewer assumptions than state tomography.

Security proofs for QKD are established without measurement assumptions.

Detector inefficiencies impact entanglement certification and QKD security.

Abstract

We address the question of how much entanglement can be certified from the observed correlations and the knowledge of the Hilbert space dimension of the measured systems. We focus on the case in which both systems are known to be qubits. For several correlations (though not for all), one can certify the same amount of entanglement as with state tomography, but with fewer assumptions, since nothing is assumed about the measurements. We also present security proofs of quantum key distribution without any assumption on the measurements. We discuss how both the amount of entanglement and the security of quantum key distribution (QKD) are affected by the inefficiency of detectors in this scenario.