Direct probing of the Wigner function by time-multiplexed detection of photon statistics

TL;DR

This paper demonstrates a loss-tolerant method for directly probing the Wigner function of non-Gaussian quantum states using time-multiplexed photon detection, offering an alternative to homodyne tomography.

Contribution

It introduces a novel approach for quantum state characterization that is robust against losses and mode mismatch, using photon-number resolving detection and displacement operations.

Findings

High losses can be tolerated within certain parameters.

Mode mismatch produces a distinct signature in photon number oscillations.

Monte Carlo simulations confirm the feasibility of the method.

Abstract

We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon parity measurements and displacement operations, replacing the conventional homodyne tomography. Our emphasis lies on reconstructing the Wigner function of non-Gaussian Fock states with highly negative values in a scheme that is based on a realistic experimental setup. In order to establish the concept of loss-tolerance for state characterization we show how losses can be decoupled from the impact of other experimental imperfections, i.e. the non-unity transmittance of the displacement beamsplitter and non-ideal mode overlap. We relate the experimentally accessible parameters to effective ones that are needed for an optimised state reconstruction. The feasibility of our approach is tested by Monte Carlo simulations, which provide bounds resulting from statistical errors that are due to limited data sets. Our results clearly show that high losses can be accepted for a defined parameter range, and moreover, that (in contrast to homodyne detection) mode mismatch results in a distinct signature, which can be evaluated by analysing the photon number oscillations of the displaced Fock states.