Classical analogs of generalized purities, entropies, and logarithmic negativity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913751890919424 |
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| author | Díaz, Bogar González, Diego Hernández, Marcos J. Vergara, J. David |
| author_facet | Díaz, Bogar González, Diego Hernández, Marcos J. Vergara, J. David |
| contents | It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classical analogs of generalized purities, entropies, and logarithmic negativity Díaz, Bogar González, Diego Hernández, Marcos J. Vergara, J. David Quantum Physics Mathematical Physics Classical Physics It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information. |
| title | Classical analogs of generalized purities, entropies, and logarithmic negativity |
| topic | Quantum Physics Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2305.02887 |