Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers

TL;DR

This paper presents a practical interferometric method to measure local invariants of two-qubit states, enabling efficient detection of Bell nonlocality and potential applications in quantum secret sharing.

Contribution

It introduces a direct measurement technique for two-qubit invariants using Hong-Ou-Mandel interference, improving resource efficiency over previous methods.

Findings

Measuring 3 invariants suffices to determine Bell inequality violation.

Hong-Ou-Mandel interference enables faster invariant measurement.

Nonlocal measurement strategy is more resource-efficient than local strategies.

Abstract

We describe a direct method to experimentally determine local two-qubit invariants by performing interferometric measurements on multiple copies of a given two-qubit state. We use this framework to analyze two different kinds of two-qubit invariants of Makhlin and Jing et. al. These invariants allow to fully reconstruct any two-qubit state up to local unitaries. We demonstrate that measuring 3 invariants is sufficient to find, e.g., the optimal Bell inequality violation. These invariants can be measured with local or nonlocal measurements. We show that the nonlocal strategy that follows from Makhlin's invariants is more resource-efficient than local strategy following from the invariants of Jing et al. To measure all of the Makhlin's invariants directly one needs to use both two-qubit singlet and three-qubit W-state projections on multiple copies of the two-qubit state. This problem is equivalent to a cordinate system handness measurement. We demonstrate that these 3-qubit measurements can be performed by utilizing Hong-Ou-Mandel interference which gives significant speedup in comparison to the classical handness measurement. Finally, we point to potential application of our results in quantum secret sharing.