Practical and Efficient Verification of Entanglement with Incomplete Measurement Settings

TL;DR

This paper introduces a practical framework for verifying entanglement using limited measurement data, employing optimized witnesses and demonstrating effectiveness in photon-polarization experiments.

Contribution

It develops an efficient method to verify entanglement with incomplete measurements by constructing witnesses via semidefinite programming, validated experimentally.

Findings

Entanglement can be certified with limited measurement data.

The approach outperforms traditional methods in resource-limited scenarios.

Experimental results confirm the method's practicality with photon-polarization qubits.

Abstract

In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how the experimental estimation of a small number of observables can be directly exploited to construct a large family of entanglement witnesses, enabling the efficient identification of entangled states. Moreover, we introduce an optimization approach, formulated as a semidefinite program, that systematically searches for those witnesses best suited to reveal entanglement under the given measurement constraints. We demonstrate the practicality of the approach in a proof-of-principle experiment with photon-polarization qubits, where entanglement is certified using only a fraction of the full measurement data. These results reveal the maximal usefulness of incomplete measurement settings for entanglement verification in realistic scenarios.