Homodyne Detection of Temporally Resolved Quantum States

TL;DR

This paper develops a formalism and algorithm for measuring and reconstructing temporally resolved quantum states using balanced homodyne detection, accounting for realistic measurement errors.

Contribution

It introduces a new formalism and simulation algorithm for time-resolved quantum state measurement with homodyne detection, including practical error considerations.

Findings

Effective simulation of photocurrent in time-resolved homodyne detection

Analysis of measurement errors on quantum state reconstruction

Open source implementation of the proposed method

Abstract

We present an analysis of the time domain measurement of temporally resolvable quantum states using balanced homodyne detection. Our approach outlines a formalism of detecting quantum states in arbitrary temporal modes via projection of the temporal mode onto a natural detector basis. We then present an algorithm for simulating the resultant photocurrent of continuous homodyne detection in the presence of a temporally resolved mode, and use this algorithm to explore the effects of realistic measurement errors on marginal reconstruction and quantum state tomography. A complete implementation of the method is provided through open source code on a GitHub repository.