Optimal local oscillators for the homodyne detection of multiphoton states
Abstract
We propose a framework for optimizing pulsed local oscillators (LO) for homodyne detection of multiphoton-number states by exploiting the tensor structure of their joint-spectral amplitude (JSA). We show that finding the optimal LO is equivalent to computing the JSA tensor's leading unitary eigenpair and that the factor matrices of the JSA's Tucker higher-order singular value decomposition (HOSVD) coincide with the Schmidt modes of the photon number state's single-particle reduced density matrix. We use the HOSVD to bound the optimal homodyne visibility and to initialize gradient based optimization. In simulated JSAs, weakly correlated, few-mode states reach near-unity visibility, with the leading HOSVD mode being the optimal LO, while strongly correlated, multimode states require full optimization and saturate below unit visibility even at the true optimum. These results offer a practical route to design LOs for homodyne detection experiments with realistic sources of photon-number states, which contributes to the practical implementation of sources of non-Gaussian quantum states.
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BibTeX
@misc{osorio2026optimal,
title = {{Optimal local oscillators for the homodyne detection of multiphoton states}},
author = {Gisell Lorena Osorio and Paul Virally and Sean Molesky and Nicolás Quesada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28133},
eprint = {2609.28133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28133},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal local oscillators for the homodyne detection of multiphoton states
AU - Gisell Lorena Osorio
AU - Paul Virally
AU - Sean Molesky
AU - Nicolás Quesada
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28133
UR - https://arxiv.org/abs/2609.28133
AB - We propose a framework for optimizing pulsed local oscillators (LO) for homodyne detection of multiphoton-number states by exploiting the tensor structure of their joint-spectral amplitude (JSA). We show that finding the optimal LO is equivalent to computing the JSA tensor's leading unitary eigenpair and that the factor matrices of the JSA's Tucker higher-order singular value decomposition (HOSVD) coincide with the Schmidt modes of the photon number state's single-particle reduced density matrix. We use the HOSVD to bound the optimal homodyne visibility and to initialize gradient based optimization. In simulated JSAs, weakly correlated, few-mode states reach near-unity visibility, with the leading HOSVD mode being the optimal LO, while strongly correlated, multimode states require full optimization and saturate below unit visibility even at the true optimum. These results offer a practical route to design LOs for homodyne detection experiments with realistic sources of photon-number states, which contributes to the practical implementation of sources of non-Gaussian quantum states.
ER -