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

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.

22 pages, 13 figures, published version

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• Experimental quantification of coherence of a tunable quantum detector
• Producing high fidelity single photons with optimal brightness via waveguided parametric down-conversion
• Mesoscopic ultrafast nonlinear optics -- The emergence of multimode quantum non-Gaussian physics
• Tomography by noise
• Self-consistent phase determination for Wigner function reconstruction
• Characteristics of displaced single photons attained via higher order factorial moments
• Implementable Hybrid Entanglement Witness
• Hacking coherent-one-way quantum key distribution with present-day technology
• Reduced state of the field and classicality of quantum Gaussian evolution
• Quantum non-Gaussian high Fock states of light pulses and their superpositions
• Advancing the heralded photon-number-state characterization by understanding the interplay of experimental settings