Overcomplete quantum tomography of a path-entangled two-photon state

TL;DR

This paper presents a novel method for quantum tomography of path-entangled two-photon states, utilizing an overcomplete data set and an ancilla mode to accurately measure quantum states generated by semiconductor quantum dots.

Contribution

It introduces an overcomplete quantum tomography technique with an ancilla mode for path-entangled two-photon states, improving accuracy and revealing hidden coherences.

Findings

Successfully measured the density matrix of two-photon path-entangled states.

Demonstrated that overcomplete data sets can uncover hidden spatial coherences.

Identified the main source of imperfect fidelity in the generated entangled states.

Abstract

Path-entangled N-photon states can be obtained through the coalescence of indistinguishable photons inside linear networks. They are key resources for quantum enhanced metrology, quantum imaging, as well as quantum computation based on quantum walks. However, the quantum tomography of path-entangled indistinguishable photons is still in its infancy as it requires multiple phase estimations increasing rapidly with N. Here, we propose and implement a method to measure the quantum tomography of path-entangled two-photon states. A two-photon state is generated through the Hong-Ou-Mandel interference of highly indistinguishable single photons emitted by a semiconductor quantum dot-cavity device. To access both the populations and the coherences of the path-encoded density matrix, we introduce an ancilla spatial mode and perform photon correlations as a function of a single phase in a split Mach-Zehnder interferometer. We discuss the accuracy of standard quantum tomography techniques and show that an overcomplete data set can reveal spatial coherences that could be otherwise hidden due to limited or noisy statistics. Finally, we extend our analysis to extract the truly indistinguishable part of the density matrix, which allows us to identify the main origin for the imperfect fidelity to the maximally entangled state.