Quantum dynamics as a pseudo-density matrix
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910921016737792 |
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| author | Fullwood, James |
| author_facet | Fullwood, James |
| contents | While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently it was emphasized in the work of Fitzsimons, Jones and Vedral that if such a state over time is to encode not only spatial but also temporal correlations which exist within a quantum dynamical process, then it should be represented not by a density matrix, but rather, by a pseudo-density matrix. A pseudo-density matrix is a hermitian matrix of unit trace whose marginals are density matrices, and in this work, we make use a factorization system for quantum channels to associate a pseudo-density matrix with a quantum system which is to evolve according to a finite sequence of quantum channels. We then view such a pseudo-density matrix as the quantum analog of a local patch of spacetime, and we make an in-depth mathematical analysis of such quantum dynamical pseudo-density matrices and the properties they satisfy. We also show how to explicitly extract quantum dynamics from a given pseudo-density matrix, thus solving an open problem posed in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03954 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum dynamics as a pseudo-density matrix Fullwood, James Quantum Physics While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently it was emphasized in the work of Fitzsimons, Jones and Vedral that if such a state over time is to encode not only spatial but also temporal correlations which exist within a quantum dynamical process, then it should be represented not by a density matrix, but rather, by a pseudo-density matrix. A pseudo-density matrix is a hermitian matrix of unit trace whose marginals are density matrices, and in this work, we make use a factorization system for quantum channels to associate a pseudo-density matrix with a quantum system which is to evolve according to a finite sequence of quantum channels. We then view such a pseudo-density matrix as the quantum analog of a local patch of spacetime, and we make an in-depth mathematical analysis of such quantum dynamical pseudo-density matrices and the properties they satisfy. We also show how to explicitly extract quantum dynamics from a given pseudo-density matrix, thus solving an open problem posed in the literature. |
| title | Quantum dynamics as a pseudo-density matrix |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2304.03954 |