On the complex zeros of the wavefunction
Abstract
The Schrödinger wavefunction is ubiquitous in quantum mechanics, quantum chemistry, and bosonic quantum information theory. Its zero-set for fermionic systems is well-studied and central for determining chemical properties, yet for bosonic systems the zero-set is less understood, especially in the context of characterizing non-classicality. Here we study the zeros of such wavefunctions and give them a novel information-theoretic interpretation. Our main technical result is showing that the wavefunction of most bosonic quantum systems can be extended to a holomorphic function over the complex plane, allowing the application of powerful techniques from complex analysis. As a consequence, we prove a version of Hudson's theorem for the wavefunction and characterize Gaussian dynamics as classical motion of the wavefunction zeros. Our findings suggest that the non-Gaussianity of quantum optical states can be detected by measuring a single quadrature of the electromagnetic field, which we demonstrate in a companion paper [arXiv:2507.23005]. More generally, our results show that the non-Gaussian features of bosonic quantum systems are encoded in the zeros of their wavefunction.
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BibTeX
@misc{cerf2026complex,
title = {{On the complex zeros of the wavefunction}},
author = {Sacha Cerf and Clara Wassner and Jack Davis and Francesco Arzani and Ulysse Chabaud},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2507.23468},
eprint = {2507.23468},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05732599v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the complex zeros of the wavefunction
AU - Sacha Cerf
AU - Clara Wassner
AU - Jack Davis
AU - Francesco Arzani
AU - Ulysse Chabaud
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2507.23468
UR - https://hal.science/hal-05732599v1
AB - The Schrödinger wavefunction is ubiquitous in quantum mechanics, quantum chemistry, and bosonic quantum information theory. Its zero-set for fermionic systems is well-studied and central for determining chemical properties, yet for bosonic systems the zero-set is less understood, especially in the context of characterizing non-classicality. Here we study the zeros of such wavefunctions and give them a novel information-theoretic interpretation. Our main technical result is showing that the wavefunction of most bosonic quantum systems can be extended to a holomorphic function over the complex plane, allowing the application of powerful techniques from complex analysis. As a consequence, we prove a version of Hudson's theorem for the wavefunction and characterize Gaussian dynamics as classical motion of the wavefunction zeros. Our findings suggest that the non-Gaussianity of quantum optical states can be detected by measuring a single quadrature of the electromagnetic field, which we demonstrate in a companion paper [arXiv:2507.23005]. More generally, our results show that the non-Gaussian features of bosonic quantum systems are encoded in the zeros of their wavefunction.
ER -