Quantum networks theory
- URL: http://arxiv.org/abs/2110.10587v2
- Date: Wed, 13 Jul 2022 17:02:31 GMT
- Title: Quantum networks theory
- Authors: Pablo Arrighi, Am\'elia Durbec, Matt Wilson
- Abstract summary: The formalism of quantum theory over discrete systems is extended in two significant ways.
tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates.
quantum evolutions are generalized to act over network configurations.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The formalism of quantum theory over discrete systems is extended in two
significant ways. First, tensors and traceouts are generalized, so that systems
can be partitioned according to almost arbitrary logical predicates in a robust
manner. Second, quantum evolutions are generalized to act over network
configurations, in such a way that nodes be allowed to merge, split and
reconnect coherently in a superposition. 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 partitioning of systems becomes both logical and dynamical. Such
interrelations in fact carry through, albeit two new notions become
instrumental: consistency and comprehension.
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