Quadrature Histograms in Maximum Likelihood Quantum State Tomography

TL;DR

This paper demonstrates that discretizing continuous variable homodyne measurements into quadrature histograms with optimized bin widths can significantly reduce computational costs in quantum state tomography without substantially affecting the fidelity of the estimated quantum state.

Contribution

The paper introduces strategies for choosing histogram bin widths in quadrature measurements, enabling efficient quantum state tomography with minimal fidelity loss.

Findings

Optimized histogram bin widths reduce computation time.

Discretization minimally impacts state fidelity.

Integration over bins maintains high tomography accuracy.

Abstract

Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state and the true state. This paper studies different strategies for determining the histogram bin widths. We show that computation time can be significantly reduced with little loss in the fidelity of the estimated state when the measurement operators corresponding to each histogram bin are integrated over the bin width.