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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Main Authors: Pablo Arrighi, Amélia Durbec, Matt Wilson
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2024-10-01
Series:Quantum
Online Access:https://quantum-journal.org/papers/q-2024-10-23-1508/pdf/
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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.
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publishDate 2024-10-01
publisher Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
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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/
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AT ameliadurbec quantumnetworkstheory
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