Quantum networks theory
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and r...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-10-23-1508/pdf/ |
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| _version_ | 1850207354052673536 |
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| author | Pablo Arrighi Amélia Durbec Matt Wilson |
| author_facet | Pablo Arrighi Amélia Durbec Matt Wilson |
| author_sort | Pablo Arrighi |
| collection | DOAJ |
| description | The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and reconnect coherently in a superposition. Second, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the neighbourhood and partitioning between systems become both quantum, dynamical, and logical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension. |
| format | Article |
| id | doaj-art-28a3f16092a24023b8a15ee14ad1ff88 |
| institution | OA Journals |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-28a3f16092a24023b8a15ee14ad1ff882025-08-20T02:10:32ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-10-018150810.22331/q-2024-10-23-150810.22331/q-2024-10-23-1508Quantum networks theoryPablo ArrighiAmélia DurbecMatt WilsonThe formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and reconnect coherently in a superposition. Second, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the neighbourhood and partitioning between systems become both quantum, dynamical, and logical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.https://quantum-journal.org/papers/q-2024-10-23-1508/pdf/ |
| spellingShingle | Pablo Arrighi Amélia Durbec Matt Wilson Quantum networks theory Quantum |
| title | Quantum networks theory |
| title_full | Quantum networks theory |
| title_fullStr | Quantum networks theory |
| title_full_unstemmed | Quantum networks theory |
| title_short | Quantum networks theory |
| title_sort | quantum networks theory |
| url | https://quantum-journal.org/papers/q-2024-10-23-1508/pdf/ |
| work_keys_str_mv | AT pabloarrighi quantumnetworkstheory AT ameliadurbec quantumnetworkstheory AT mattwilson quantumnetworkstheory |