On the complex zeros of the wavefunction

• URL: http://arxiv.org/abs/2507.23468v2
• Date: Fri, 01 Aug 2025 12:26:09 GMT
• Title: On the complex zeros of the wavefunction
• Authors: Sacha Cerf, Clara Wassner, Jack Davis, Francesco Arzani, Ulysse Chabaud,
• Abstract summary: We study the zeros of such wavefunctions and give them a novel information-theoretic interpretation.<n>Our results show that the non-Gaussian features of bosonic quantum systems are encoded in the zeros of their wavefunction.
• Score: 0.5242869847419834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Schr\"odinger 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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