Reversibility and the structure of the local state space
The richness of quantum theory’s reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory’s reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2015-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/12/123001 |
| _version_ | 1797751035353104384 |
|---|---|
| author | Sabri W Al-Safi Jonathan Richens |
| author_facet | Sabri W Al-Safi Jonathan Richens |
| author_sort | Sabri W Al-Safi |
| collection | DOAJ |
| description | The richness of quantum theory’s reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory’s reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these features, demonstrating that reversibility places strong constraints on both the local and global state space. Firstly, we show that all reversible dynamics are trivial (composed of local transformations and permutations of subsytems) in maximally non-local theories whose local state spaces satisfy a dichotomy criterion; this applies to a range of operational models that have previously been studied, such as d -dimensional ‘hyperballs’ and almost all regular polytope systems. By separately deriving a similar result for odd-sided polygons, we show that classical systems are the only regular polytope state spaces whose maximally non-local composites allow for non-trivial reversible dynamics. Secondly, we show that non-trivial reversible dynamics do exist in maximally non-local theories whose state spaces are reducible into two or more smaller spaces. We conjecture that this is a necessary condition for the existence of such dynamics, but that reversible entanglement generation remains impossible even in this scenario. |
| first_indexed | 2024-03-12T16:42:34Z |
| format | Article |
| id | doaj.art-7cc2d0c707bf44f7bfec1d00dd4bf986 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:42:34Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-7cc2d0c707bf44f7bfec1d00dd4bf9862023-08-08T14:24:33ZengIOP PublishingNew Journal of Physics1367-26302015-01-01171212300110.1088/1367-2630/17/12/123001Reversibility and the structure of the local state spaceSabri W Al-Safi0Jonathan Richens1School of Science & Technology, Nottingham Trent University , Burton Street, Nottingham NG1 4BU, UKControlled Quantum Dynamics Theory Group, Department of Physics , Imperial College London, London SW7 2AZ, UKThe richness of quantum theory’s reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory’s reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these features, demonstrating that reversibility places strong constraints on both the local and global state space. Firstly, we show that all reversible dynamics are trivial (composed of local transformations and permutations of subsytems) in maximally non-local theories whose local state spaces satisfy a dichotomy criterion; this applies to a range of operational models that have previously been studied, such as d -dimensional ‘hyperballs’ and almost all regular polytope systems. By separately deriving a similar result for odd-sided polygons, we show that classical systems are the only regular polytope state spaces whose maximally non-local composites allow for non-trivial reversible dynamics. Secondly, we show that non-trivial reversible dynamics do exist in maximally non-local theories whose state spaces are reducible into two or more smaller spaces. We conjecture that this is a necessary condition for the existence of such dynamics, but that reversible entanglement generation remains impossible even in this scenario.https://doi.org/10.1088/1367-2630/17/12/123001generalized probabilistic theoriesreversibilityentanglementfoundations |
| spellingShingle | Sabri W Al-Safi Jonathan Richens Reversibility and the structure of the local state space New Journal of Physics generalized probabilistic theories reversibility entanglement foundations |
| title | Reversibility and the structure of the local state space |
| title_full | Reversibility and the structure of the local state space |
| title_fullStr | Reversibility and the structure of the local state space |
| title_full_unstemmed | Reversibility and the structure of the local state space |
| title_short | Reversibility and the structure of the local state space |
| title_sort | reversibility and the structure of the local state space |
| topic | generalized probabilistic theories reversibility entanglement foundations |
| url | https://doi.org/10.1088/1367-2630/17/12/123001 |
| work_keys_str_mv | AT sabriwalsafi reversibilityandthestructureofthelocalstatespace AT jonathanrichens reversibilityandthestructureofthelocalstatespace |