Quantified convergence of general homodyne measurements with applications to continuous variable quantum computing

TL;DR

This paper quantifies how standard and broadband pulsed homodyne measurements converge to ideal quadrature measurements, providing bounds on measurement fidelity relevant for continuous variable quantum computing applications.

Contribution

It introduces quantitative bounds on the fidelity of homodyne measurements, extending previous work to broadband pulsed homodyne and practical quantum computing scenarios.

Findings

Derived lower bounds on measurement fidelity depending on LO amplitude and moments of number operators.

Demonstrated bounds' relevance for quantum teleportation and GKP error correction.

Showed convergence properties of broadband pulsed homodyne to ideal quadrature measurements.

Abstract

In arXiv:2503.00188 we introduced broadband pulsed (BBP) homodyne measurements as a generalization of standard pulsed homodyne quadrature measurements. BBP can take advantage of detectors such as calorimeters that have the potential for high efficiency over a broad spectral range. BBP homodyne retains the advantages of standard pulsed homodyne, enabling measurement of arbitrary quadratures in the limit of large amplitude local oscillators (LO). Here we quantify the convergence of standard and BBP homodyne quadrature measurements to those of the quadrature of interest. We obtain lower bounds on the fidelity of the post-measurement classical-quantum state of outcomes and unmeasured modes, and the fidelity of the states obtained after applying operations conditional on measurement outcomes. The bounds depend on the LO amplitude and the moments of number operators. We demonstrate the practical relevance of these bounds by evaluating them for standard pulsed homodyne used for estimating values of the characteristic function of the Wigner distribution, expectations of moments, for quantum teleportation and for continuous variable error correction with GKP codes.