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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.12132 |
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| _version_ | 1866910050693414912 |
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| author | Lomoc, F. Canosa, N. Boette, A. P. Rossignoli, R. |
| author_facet | Lomoc, F. Canosa, N. Boette, A. P. Rossignoli, R. |
| contents | We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12132 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | History state formalism for time series with application to finance Lomoc, F. Canosa, N. Boette, A. P. Rossignoli, R. Quantum Physics We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures. |
| title | History state formalism for time series with application to finance |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.12132 |