Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference

TL;DR

This paper presents a direct, efficient optical method to measure and witness quantum entanglement in arbitrary two-qubit states using minimal interferometric measurements, avoiding full state tomography.

Contribution

The authors introduce a novel interferometric approach that directly measures entanglement negativity with fewer measurements than traditional quantum state tomography.

Findings

Negativity can be measured with 11 specific measurements on multiple copies.

The method applies the Peres-Horodecki criterion directly.

Measuring negativity requires 13 multicopy projections of Makhlin's invariants.

Abstract

We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of 9 Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate that these invariants are both a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.