{"title":"量子态随时间变化的一般协方差","authors":"James Fullwood","doi":"10.1007/s11005-024-01870-4","DOIUrl":null,"url":null,"abstract":"<div><p>Quantum states over time are a spatiotemporal generalization of density operators which were first introduced to give a more even-handed treatment of space and time in quantum theory. In particular, quantum states over time encode not only spatial, but also <i>causal</i> correlations associated with the dynamical evolution of a quantum system, and the association of quantum states over time with the dynamical flow of quantum information is in direct analogy with spacetime and its relation to classical dynamics. In this work, we further such an analogy by formulating a notion of general covariance for the theory of quantum states over time. We then associate a canonical state over time with a density operator which is to evolve under a sequence of quantum processes modeled by completely positive trace-preserving (CPTP) maps, and we show that such a canonical state over time satisfies such a notion of covariance. We also show that the dynamical quantum Bayes’ rule transforms covariantly with respect to quantum states over time, and we conclude with a discussion of what it means for a physical law to be generally covariant when formulated in terms of quantum states over time.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"General covariance for quantum states over time\",\"authors\":\"James Fullwood\",\"doi\":\"10.1007/s11005-024-01870-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Quantum states over time are a spatiotemporal generalization of density operators which were first introduced to give a more even-handed treatment of space and time in quantum theory. In particular, quantum states over time encode not only spatial, but also <i>causal</i> correlations associated with the dynamical evolution of a quantum system, and the association of quantum states over time with the dynamical flow of quantum information is in direct analogy with spacetime and its relation to classical dynamics. In this work, we further such an analogy by formulating a notion of general covariance for the theory of quantum states over time. We then associate a canonical state over time with a density operator which is to evolve under a sequence of quantum processes modeled by completely positive trace-preserving (CPTP) maps, and we show that such a canonical state over time satisfies such a notion of covariance. We also show that the dynamical quantum Bayes’ rule transforms covariantly with respect to quantum states over time, and we conclude with a discussion of what it means for a physical law to be generally covariant when formulated in terms of quantum states over time.\\n</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"114 6\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01870-4\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01870-4","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Quantum states over time are a spatiotemporal generalization of density operators which were first introduced to give a more even-handed treatment of space and time in quantum theory. In particular, quantum states over time encode not only spatial, but also causal correlations associated with the dynamical evolution of a quantum system, and the association of quantum states over time with the dynamical flow of quantum information is in direct analogy with spacetime and its relation to classical dynamics. In this work, we further such an analogy by formulating a notion of general covariance for the theory of quantum states over time. We then associate a canonical state over time with a density operator which is to evolve under a sequence of quantum processes modeled by completely positive trace-preserving (CPTP) maps, and we show that such a canonical state over time satisfies such a notion of covariance. We also show that the dynamical quantum Bayes’ rule transforms covariantly with respect to quantum states over time, and we conclude with a discussion of what it means for a physical law to be generally covariant when formulated in terms of quantum states over time.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.