Quantum dynamics as a pseudo-density matrix

James Fullwood

doi:10.22331/q-2025-04-24-1719

Quantum dynamics as a pseudo-density matrix

School of Mathematics and Statistics, Hainan University, 58 Renmin Ave., 570228, Haikou, Hainan Province, China

Published:	2025-04-24, volume 9, page 1719
Editor:	Ángela Capel
Eprint:	arXiv:2304.03954v4
Doi:	https://doi.org/10.22331/q-2025-04-24-1719
Citation:	Quantum 9, 1719 (2025).

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Abstract

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 $\textit{pseudo-density matrix}$. 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.

► BibTeX data

@article{Fullwood2025quantumdynamicsas,
  doi = {10.22331/q-2025-04-24-1719},
  url = {https://doi.org/10.22331/q-2025-04-24-1719},
  title = {Quantum dynamics as a pseudo-density matrix},
  author = {Fullwood, James},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1719},
  month = apr,
  year = {2025}
}

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Cited by

[1] Yi Guo and Shunlong Luo, "Temporal correlating power of quantum channels", Physical Review A 111 6, 062415 (2025).

[2] Minjeong Song and Arthur J. Parzygnat, "Bipartite quantum states admitting a causal explanation", AVS Quantum Science 7 4, 045002 (2025).

[3] Yuxuan Zheng, Xinfang Nie, Hongfeng Liu, Yutong Luo, Dawei Lu, and Xiangjing Liu, "Experimental virtual quantum broadcasting", Physical Review A 111 6, L060402 (2025).

[4] Seok Hyung Lie and Hyukjoon Kwon, "Probing Quantum States over Spacetime through Interferometry", Physical Review Letters 136 25, 250201 (2026).

[5] Arthur J. Parzygnat and James Fullwood, "Time‐Symmetric Correlations for Open Quantum Systems", Annalen der Physik 537 12, e00221 (2025).

[6] Seok Hyung Lie and James Fullwood, "Multipartite Quantum States over Time from Two Fundamental Assumptions", Physical Review Letters 135 23, 230204 (2025).

[7] Ovidiu Racorean, "Eternal black holes and temporal quantum correlations", arXiv:2304.00982, (2023).

[8] Arthur J. Parzygnat, James Fullwood, Francesco Buscemi, and Giulio Chiribella, "Virtual Quantum Broadcasting", Physical Review Letters 132 11, 110203 (2024).

[9] Seok Hyung Lie and Nelly H. Y. Ng, "Quantum state over time is unique", Physical Review Research 6 3, 033144 (2024).

[10] Xiangjing Liu, Qian Chen, and Oscar Dahlsten, "Inferring the arrow of time in quantum spatiotemporal correlations", Physical Review A 109 3, 032219 (2024).

[11] Minjeong Song, Varun Narasimhachar, Bartosz Regula, Thomas J. Elliott, and Mile Gu, "Causal Classification of Spatiotemporal Quantum Correlations", Physical Review Letters 133 11, 110202 (2024).

[12] Zhian Jia, Minjeong Song, and Dagomir Kaszlikowski, "Quantum space-time marginal problem: global causal structure from local causal information", New Journal of Physics 25 12, 123038 (2023).

[13] Zhen Wu, Arthur J. Parzygnat, Vlatko Vedral, and James Fullwood, "Quantum mutual information in time", New Journal of Physics 27 6, 064504 (2025).

[14] James Fullwood and Arthur J. Parzygnat, "On dynamical measures of quantum information", arXiv:2306.01831, (2023).

[15] Arthur J. Parzygnat and James Fullwood, "Time-symmetric correlations for open quantum systems", arXiv:2407.11123, (2024).

[16] Zhian Jia and Dagomir Kaszlikowski, "The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes", arXiv:2305.15649, (2023).

[17] Ovidiu Racorean, "The non-orientable spacetime of the eternal black hole", Physics Letters B 868, 139767 (2025).

[18] Mia Stamatova and Vlatko Vedral, "Complex Heat Capacity as a Witness of Spatio-Temporal Entanglement", arXiv:2508.15728, (2025).

[19] Yuxuan Zheng, Xinfang Nie, Hongfeng Liu, Yutong Luo, Dawei Lu, and Xiangjing Liu, "Experimental Virtual Quantum Broadcasting", arXiv:2501.11390, (2025).

[20] Mark M. Wilde, "Fundamentals of quantum Boltzmann machine learning with visible and hidden units", arXiv:2512.19819, (2025).

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