Dynamics of Quantum Causal Structures
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, because of quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laborat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2018-03-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.8.011047 |
| _version_ | 1818691323494924288 |
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| author | Esteban Castro-Ruiz Flaminia Giacomini Časlav Brukner |
| author_facet | Esteban Castro-Ruiz Flaminia Giacomini Časlav Brukner |
| author_sort | Esteban Castro-Ruiz |
| collection | DOAJ |
| description | It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, because of quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite (e.g., one cannot say whether operation in laboratory A occurs before or after operation in laboratory B). Here, we develop a framework for “dynamics of causal structures,” i.e., for transformations of process matrices into process matrices. We show that, under continuous and reversible transformations, the causal order between operations is always preserved. However, the causal order between a subset of operations can be changed under continuous yet nonreversible transformations. An explicit example is that of the quantum switch, where a party in the past affects the causal order of operations of future parties, leading to a transition from a channel from A to B, via superposition of causal orders, to a channel from B to A. We generalize our framework to construct a hierarchy of quantum maps based on transformations of process matrices and transformations thereof. |
| first_indexed | 2024-12-17T12:40:04Z |
| format | Article |
| id | doaj.art-8dae83f8453e4dd387b8080b3da66dba |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-17T12:40:04Z |
| publishDate | 2018-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-8dae83f8453e4dd387b8080b3da66dba2022-12-21T21:48:03ZengAmerican Physical SocietyPhysical Review X2160-33082018-03-018101104710.1103/PhysRevX.8.011047Dynamics of Quantum Causal StructuresEsteban Castro-RuizFlaminia GiacominiČaslav BruknerIt was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, because of quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite (e.g., one cannot say whether operation in laboratory A occurs before or after operation in laboratory B). Here, we develop a framework for “dynamics of causal structures,” i.e., for transformations of process matrices into process matrices. We show that, under continuous and reversible transformations, the causal order between operations is always preserved. However, the causal order between a subset of operations can be changed under continuous yet nonreversible transformations. An explicit example is that of the quantum switch, where a party in the past affects the causal order of operations of future parties, leading to a transition from a channel from A to B, via superposition of causal orders, to a channel from B to A. We generalize our framework to construct a hierarchy of quantum maps based on transformations of process matrices and transformations thereof.http://doi.org/10.1103/PhysRevX.8.011047 |
| spellingShingle | Esteban Castro-Ruiz Flaminia Giacomini Časlav Brukner Dynamics of Quantum Causal Structures Physical Review X |
| title | Dynamics of Quantum Causal Structures |
| title_full | Dynamics of Quantum Causal Structures |
| title_fullStr | Dynamics of Quantum Causal Structures |
| title_full_unstemmed | Dynamics of Quantum Causal Structures |
| title_short | Dynamics of Quantum Causal Structures |
| title_sort | dynamics of quantum causal structures |
| url | http://doi.org/10.1103/PhysRevX.8.011047 |
| work_keys_str_mv | AT estebancastroruiz dynamicsofquantumcausalstructures AT flaminiagiacomini dynamicsofquantumcausalstructures AT caslavbrukner dynamicsofquantumcausalstructures |