Reversibility vs Local Creation/Destruction

Arrighi, Pablo; Durbec, Nicolas; Emmanuel, Aurélien

doi:10.1007/978-3-030-21500-2_4

Cited by 4 publications

(5 citation statements)

References 28 publications

(39 reference statements)

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“…For instance we have shown that if U is ∀m∃n ζ m ζ n -causal, so is U 2 , see Prop. 8. But what if U is just ∀m ζ m ζ-causal?…”

Section: Summary Of Contributionsmentioning

confidence: 99%

“…Despite the need for a naming of nodes, the actual choice of naming of nodes should have no effect on the evolution of a network beyond this role: this independence is formalised by the notion of renaming-invariance. A second potential ambush is explained in [8], we must ensure that names are no obstacle to unitary node creation/destruction. Indeed, suppose that a node u splits into u and v. How can this evolution be a unitary U ?…”

Section: Contributionsmentioning

confidence: 99%

“…This was a somewhat uncomfortable situation, because the informally defined model of Hassalcher and Meyer [29] did seem to feature reversibility, vertex creation/destruction, and non-signalling causality. Again in the classical regime, the issue was finally solved by introducing a name algebra [9]. We now bring the notion of a name algebra over to the quantum regime, simplified.…”

Section: An Algebra For Naming Nodes Of Quantum Networkmentioning

confidence: 99%

See 2 more Smart Citations

Quantum networks theory

Arrighi¹,

Durbec²,

Wilson³

2021

Preprint

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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. 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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“…For instance we have shown that if U is ∀m∃n ζ m ζ n -causal, so is U 2 , see Prop. 8. But what if U is just ∀m ζ m ζ-causal?…”

Section: Summary Of Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Section: An Algebra For Naming Nodes Of Quantum Networkmentioning

confidence: 99%

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Quantum networks theory

Arrighi¹,

Durbec²,

Wilson³

2021

Preprint

Self Cite

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“…, for all permutations σ. Permutation invariance as a discrete analogue of diffeomorphism invariance is also discussed, for example, in Ref. [34].…”

Section: Why Permutation Invariance?mentioning

confidence: 99%

Background Independence and Quantum Causal Structure

Parker¹,

Costa²

2021

Preprint

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One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories. Additionally, a combination of the two theories is expected to yield non-classical, or "indefinite", causal structures. In this paper, we present a backgroundindependent formulation of the process matrix formalism-a form of quantum mechanics that allows for indefinite causal structure-while retaining operationally well-defined measurement statistics. We do this by postulating an arbitrary probability distribution of measurement outcomes across discrete 'chunks' of spacetime, which we think of as physical laboratories, and then requiring that this distribution be invariant under any permutation of laboratories. We find (a) that one still obtains nontrivial, indefinite causal structures with background independence, (b) that we lose the idea of local operations in distinct laboratories, but can recover it by encoding a reference frame into the physical states of our system, and (c) that permutation invariance imposes surprising symmetry constraints that, although formally similar to a superselection rule, cannot be interpreted as such.

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“…Overall, starting from a CA F we have defined a gauge extension F ′ which features a strong interaction between the gauge and the matter field. In the world of CA this is the first example of the kind [5,3]. Building this example required the choice of a very specific extension of the gauge-transformation over the gauge field (cf fig.4a) so as to obtain gaugeinvariance whilst preserving reversibility and injectivity.…”

mentioning

confidence: 99%

Non-abelian Gauge-Invariant Cellular Automata

Arrighi¹,

Molfetta²,

Eon³

2019

Theory and Practice of Natural Computing

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Gauge-invariance is a fundamental concept in Physics-known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata. More precisely, the notions of gauge-invariance and gauge-equivalence in Cellular Automata are formalized. A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.

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Reversibility vs Local Creation/Destruction

Cited by 4 publications

References 28 publications

Quantum networks theory

Quantum networks theory

Background Independence and Quantum Causal Structure

Non-abelian Gauge-Invariant Cellular Automata

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