FRINGE: a protocol for self-referenced quantum state estimation via photon-number-resolved interferometry

TL;DR

FRINGE is a novel quantum state tomography method using photon-number-resolved interferometry that self-references the quantum field, eliminating the need for a separate local oscillator and enabling direct reconstruction of quantum states.

Contribution

It introduces a self-referenced quantum tomography protocol based on photon-number-resolved double-slit interferometry, inspired by FROG techniques, for efficient quantum state reconstruction.

Findings

No need for a known reference or mode matching.

Compatible with commercial photon-number-resolving cameras.

Enables direct reconstruction of quantum states from self-interference data.

Abstract

We introduce a self-referenced method for quantum-state tomography of light based on photon-number-resolved double-slit interferometry. Two identical copies of the unknown quantum field illuminate laterally displaced slits, guaranteeing perfect spatiotemporal mode matching without a separate local oscillator. In the far-field, detection at transverse position $x$ is associated with a relative slit phase $\phi(x)$, and an $N$-photon event projects the detected quantum field onto a state $|N;\phi(x)\rangle$. The resulting distribution $P(N,\phi)$ is the quantum analogue of a Frequency Resolved Optical Gating (FROG) trace: whereas FROG reconstructs the classical complex spectral field $E(\omega)$ from a spectrally resolved second harmonic of a pulse with its delayed self, our measurement reconstructs the Fock-space wavefunction or density matrix from binomially weighted self-interference. The scheme requires no known or mode-matched reference and is compatible with commercially available photon-number-resolving cameras. Beyond conceptual simplicity and automatic mode matching, the FROG analogy permits direct transfer of mature ultrafast-optics methodologies (e.g., mixed-state, ptychographic, and vectorial extensions) into quantum optics, offering a versatile route to tomography of quantum photon states.