Holographic quantum imaging: reconstructing spatial properties via two-particle interference

TL;DR

This paper extends two-particle interference techniques, like Hong-Ou-Mandel, to enable full quantum state tomography of both pure and mixed states for bosons and fermions, using proposed interferometric setups.

Contribution

It generalizes existing methods to extract comprehensive quantum state information from two-particle interference, applicable to both bosonic and fermionic particles.

Findings

Theoretical framework for full quantum state tomography using two-particle interference.

Proposed interferometric setups for measuring complete sets of observables.

Extension of the Hong-Ou-Mandel effect to mixed state reconstruction.

Abstract

Two particle interference phenomena, such as the Hong-Ou-Mandel effect, are a direct manifestation of the nature of the symmetry properties of indistinguishable particles as described by quantum mechanics. The Hong-Ou-Mandel effect has recently been applied as a tool for pure state tomography of a single photon. In this article, we generalise the method to extract additional information for a pure state and extend this to the full tomography of mixed states as well. The formalism is kept general enough to apply to both boson and fermion based interferometry. Our theoretical discussion is accompanied by two proposals of interferometric setups that allow the measurement of a tomographically complete set of observables for single photon quantum states.