Bayesian homodyne and heterodyne tomography

TL;DR

This paper introduces a Bayesian quantum state tomography method for continuous-variable photonic states measured by homodyne or heterodyne detection, capable of handling arbitrary states without assuming Gaussianity, demonstrated on experimental data.

Contribution

It presents the first complete Bayesian tomography workflow for arbitrary CV states measured by homodyne or heterodyne detection, including non-Gaussian states.

Findings

Accurately reconstructed coherent, thermal, and cat states.

Excellent agreement between Bayesian estimates and theoretical models.

Framework applicable to complex CV quantum states in quantum photonics.

Abstract

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties -- including uncertainty quantification and optimality in mean-squared error -- Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian quantum state tomography workflow capable of inferring generic CV states measured by homodyne or heterodyne detection, with no assumption of Gaussianity. As examples, we demonstrate our approach on experimental coherent, thermal, and cat state data, obtaining excellent agreement between our Bayesian estimates and theoretical predictions. Our approach lays the groundwork for Bayesian estimation of highly complex CV quantum states in emerging quantum photonic platforms, such as quantum communications networks and sensors.