Quantum cellular automata and free quantum field theory

D’Ariano, Giacomo Mauro; Perinotti, Paolo

doi:10.1007/s11467-016-0616-z

Cited by 24 publications

(19 citation statements)

References 27 publications

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“…when defining a system as a succession of events. Promising and clever theories that describe events in quantum mechanics have appeared in the literature, for example [18,20,35,36,[39][40][41], but none of them satisfy all these requirements.…”

Section: Comments On the Above Desideratamentioning

confidence: 99%

A Fundamental Problem in Quantizing General Relativity

Maccone¹

2019

Found Phys

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We point out a fundamental problem that hinders the quantization of general relativity: quantum mechanics is formulated in terms of systems, typically limited in space but infinitely extended in time, while general relativity is formulated in terms of events, limited both in space and in time.Many of the problems faced while connecting the two theories stem from the difficulty in shoehorning one formulation into the other. A solution is not presented, but a list of desiderata for a quantum theory based on events is laid out.

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Section: Comments On the Above Desideratamentioning

confidence: 99%

A Fundamental Problem in Quantizing General Relativity

Maccone¹

2019

Found Phys

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“…The homogeneity condition is that every two graph vertices are indistinguishable: for every pair of vertices, there exists a permutation

π \in G

such that

π false(g false) = g^{'}

that commutes with any discrimination procedure, that is, preparation of local modes and subsequent joint measurement. This condition renders

γ (G, E)

a Cayley graph, the properties of which include regularity and vertex transitivity . The “locality” condition is that the evolution is completely determined by a prescription depending on a finite number N of systems and, so, each system interacts with a finite number of others and G is finitely presented.…”

Section: Reconstruction Of “Mechanics” From Informational Principlesmentioning

confidence: 99%

Information and the Reconstruction of Quantum Physics

Jaeger

2018

Annalen der Physik

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The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra-mathematical content. Here, a representative series of specifically information-based treatments-from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems-is reviewed.The most basic physical principle of quantum mechanics is that of state superposition: Any sum of physical state vectors is also a physical state, with these states lying in a Hilbert space or related mathematical structure; cf., for example, ref.[1]. The standard view recently has been that superposition lends striking features to quantum informationthat is, information encoded entirely via quantum systems-that are not found in its classical counterpart, that is, information encoded in classical mechanical states. The most striking of the features of the quantum state itself are those associated with entanglement, which arises with the interaction or joint appearance of systems via another basic quantum physical rule, that which assigns the tensor-product space of the linear spaces of the subsystems composing a larger system; as its consequence, quantum signal-state correlations are possible that are stronger than those between classical states-these correlations being often called "nonlocal" because they violate Bell-type inequalities and enable communication and information processing tasks to be accomplished that either cannot be done as efficiently or cannot be done at all using only classical mechanical signals; cf., for example, ref. [2].That nonclassical phenomena involving correlation can arise when quantum systems are entangled was evident early in the history of quantum mechanics to Albert Einstein [3] and to Erwin Schrödinger, [4,5] who named entanglement, even before the explorations of David Bohm, [6] John S. Bell, [7] Abner Shimony, [1] and others, for whom the understanding of nonlocal correlations was a great pursuit and who devised the first ...

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“…Refs. [12,35]) that, thanks to homogeneity, the closed paths on the graph correspond to the same sequences of colours, independently of what vertex one starts from. Thus, one can find a normal subgroup R in F , corresponding to the normal closure of the set of words w = e. The quotient F/S + is a group, that we will denote by G. In particular, the graph that we constructed starting from the FCA corresponds to a Cayley graph Γ(G, S + ).…”

Section: B Neighbourhoods and Cayley Graphs Of Groupsmentioning

confidence: 99%

“…Following Refs. [34,35], we can then rigorously associate the local modes of a homogeneous FCA with the nodes of the Cayley graph of some group G. Different FCAs, with different neighbourhood schemes, determine different Cayley graphs.…”

Section: B Neighbourhoods and Cayley Graphs Of Groupsmentioning

confidence: 99%

Scalar fermionic cellular automata on finite Cayley graphs

Perinotti

Poggiali

2018

Phys. Rev. A

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A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations. We use this condition for the classification of fermionic cellular automata (FCA) on Cayley graphs of finite groups in two simple but paradigmatic case studies. The physical properties of the solutions are discussed. Finally, features of the solutions that can be extended to the case of cellular automata on infinite graphs are analyzed.

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Quantum cellular automata and free quantum field theory

Cited by 24 publications

References 27 publications

A Fundamental Problem in Quantizing General Relativity

A Fundamental Problem in Quantizing General Relativity

Information and the Reconstruction of Quantum Physics

Scalar fermionic cellular automata on finite Cayley graphs

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