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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2507.23468 |
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| _version_ | 1866912514404515840 |
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| author | Cerf, Sacha Wassner, Clara Davis, Jack Arzani, Francesco Chabaud, Ulysse |
| author_facet | Cerf, Sacha Wassner, Clara Davis, Jack Arzani, Francesco Chabaud, Ulysse |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the complex zeros of the wavefunction Cerf, Sacha Wassner, Clara Davis, Jack Arzani, Francesco Chabaud, Ulysse Quantum Physics 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. |
| title | On the complex zeros of the wavefunction |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.23468 |