Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives

Duarte, Cristhiano; Amaral, Bárbara; Cunha, Marcelo Terra; Leifer, Matthew

doi:10.48550/arxiv.2011.10349

Cited by 3 publications

(6 citation statements)

References 36 publications

(53 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, our results are pointing out that this procedure can be generalized for different complete positive trace preserving maps as well as for different dynamics, including the cases where we have interacting quantum walks [3,6,21], and we intend to address these possibilities in future publications. Another question that immediately raises from our procedure is whether we can derive emergent local quantum channels Ẽ arising from QCA, following the procedure showed in [11,12]. If such quantum channels can be achieved, we will provide a powerful tool to generate transition functions such that noisy quantum cellular automata, as described in [2], naturally appears during the decoherence process.…”

Section: Discussionmentioning

confidence: 99%

“…Rather than verify the necessary conditions to extract the quantum channels at each coarse-grained level [11,12], here we concentrate on just one specific quantum dynamics, one map and one CG level. The Dirac equation is the quantum dynamics chosen, and the coarsegraining level is the one where the coherence disappear.…”

Section: Introductionmentioning

confidence: 99%

“…(34) Finally, recast together equations (32), ( 33) and (34), we get the final expression showed in equation (11), which is the coarse grained density operator at level L + 1. Proof.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Quantum walks via quantum cellular automata

Costa

Portugal

Melo

2018

Quantum Inf Process

View full text Add to dashboard Cite

Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with the same amount of resources (in terms of effective Hilbert space dimension), various models of quantum walks. All the algorithms developed within quantum walk models are thus directly inherited by the quantum cellular automata. The latter, however, has its structure based on local interactions between qubits, and as such it can be more suitable for present (and future) experimental implementations.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum walks via quantum cellular automata

Costa

Portugal

Melo

2018

Quantum Inf Process

View full text Add to dashboard Cite

show abstract

“…Is there any way to prove a measurement in a scenario is fundamental? Formally define the coarse-graining could give some hints about the loss of information, and some work is already being done for the case of an adequate course-graining in quantum theory [20]. We could translate to an equivalent question changing coarse-graining to a refinement of a simplicial complex, therefore in some sense, we are talking about the irreducibility of a measurement scenario.…”

Section: Definition 3 (Hypergraph Realization As a Covering)mentioning

confidence: 99%

Contextuality in the Fibration Approach and the Role of Holonomy

Montanhano¹

2021

Preprint

View full text Add to dashboard Cite

Contextuality can be understood as the impossibility to construct a globally consistent description of a model even if there is local agreement. In particular, quantum models present this property. We can describe contextuality with the fibration approach, where the scenario is represented as a simplicial complex, the fibers being the sets of outcomes, and contextuality as the non-existence of a global section in the measure fibration, allowing direct representation and formalization of the already used bundle diagrams. Using the generalization to continuous outcome fibers, we built the concept of measure fibration, showing the Fine-Abramsky-Brandenburger theorem for the fibration formalism in the case of non-finite fibers. By the Voroby'ev theorem, we argue that the dependence of contextual behavior of a model to the topology of the scenario is an open problem. We introduce a hierarchy of contextual behavior to explore it, following the construction of the simplicial complex. GHZ models show that quantum theory has all levels of the hierarchy, and we exemplify the dependence on higher homotopical groups by the tetraedron scenario, where non-trivial topology implies an increase of contextual behavior for this case. For the first level of the hierarchy, we construct the concept of connection through Markov operators for the measure bundle using the measure on fibers of contexts with two measurements and taking the case of equal fibers we can identify the outcome space as the basis of a vector space, that transform according to a group extracted from the connection. With this, it is possible to show that contextuality at the level of contexts with two measurements has a relationship with the non-triviality of the holonomy group in the frame bundle. We give examples and treat disturbing models through transition functions, generalizing the holonomy.

show abstract

“…In order to deal with this new class of phenomena, quantum channels with the output dimension smaller than the input dimension, dubbed coarse-graining channels, were used to obtain a system's effective description [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In this formalism, a coarse-graining map is thus a completely positive map…”

Section: Introductionmentioning

confidence: 99%

Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics

Vallejos,

Correia,

Obando

et al. 2022

Preprint

View full text Add to dashboard Cite

Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives

Cited by 3 publications

References 36 publications

Quantum walks via quantum cellular automata

Quantum walks via quantum cellular automata

Contextuality in the Fibration Approach and the Role of Holonomy

Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics

Contact Info

Product

Resources

About