A graph with fractional revival

Bernard, Pierre-Antoine; Chan, Ada; Loranger, Éric; Tamon, Christino; Vinet, Luc

doi:10.1016/j.physleta.2017.12.001

Cited by 20 publications

(14 citation statements)

References 21 publications

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“…where the last line follows from (2). Since this sum is even, it is not ±1, and thus we get pretty good fractional revival by Theorem 2.4.…”

Section: Ada Chan Whitney Drazen or Eisenberg Mark Kempton And Gabor Lippnermentioning

confidence: 80%

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Pretty good quantum fractional revival in paths and cycles

Chan¹,

Drazen²,

Eisenberg³

et al. 2022

Algebraic Combinatorics

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We initiate the study of pretty good quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of pretty good fractional revival in a graph in terms of the eigenvalues and eigenvectors of the adjacency matrix of a graph. This characterization follows from a lemma due to Kronecker on Diophantine approximation, and is similar to the spectral characterization of pretty good state transfer in graphs. Using this, we give complete characterizations of when pretty good fractional revival can occur in paths and in cycles. Manuscript

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“…where the last line follows from (2). Since this sum is even, it is not ±1, and thus we get pretty good fractional revival by Theorem 2.4.…”

Section: Ada Chan Whitney Drazen or Eisenberg Mark Kempton And Gabor Lippnermentioning

confidence: 80%

“…Fractional revival is important in the study of entanglement generation [6]. Fractional revival in weighted paths is studied in [2,6,7,9,13,14]. In simple, unweighted paths, it has been shown that fractional revival can occur between two nodes only in paths of length 2, 3, or 4 [6].…”

Section: Introductionmentioning

confidence: 99%

Pretty good quantum fractional revival in paths and cycles

Chan¹,

Drazen²,

Eisenberg³

et al. 2022

Algebraic Combinatorics

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“…We shall call this graph ordered Hamming graph (of depth 2). Now, following [4,11], we consider the projection of the quantum walk on the ordered Hamming graph G α,β to the "column subspaces" to identify the corresponding spin lattice.…”

Section: Special Weighted Graphs and Their Projectionsmentioning

confidence: 99%

Quantum walks on graphs of the ordered Hamming scheme and spin networks

Miki¹,

Tsujimoto

Vinet

2019

SciPost Phys.

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It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.

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“…Apart from the full revival at t = T and the mirror revival at t = T /2, there is also fractional revival [35,36,38] occurring at times t = (α/β) (T /2), where α and β are coprime integers. As we shall see, the wave function…”

Section: B Fractional Revivalmentioning

confidence: 99%

“…Experimentally, the properties of quantum carpets have been illustrated in a wide class of systems, for example, Rydberg atom [31], optical lat- * songxk@sustc.edu.cn † yung@sustc.edu.cn tice [32], cavity quantum electrodynamic systems [33], optical waveguide [34], and so on. Apart from the full revival of the initial wave function, the time evolution in a quantum carpet also contains solutions cloning initial wave functions throughout the well -a phenomena called "fractional revival" [35][36][37][38]. It originates from the the phase alignment with non-adjacent eigenstates.…”

Section: Introductionmentioning

confidence: 99%

Ordered space-time structures: Quantum carpets from Gaussian sum theory

Xiong

Song

Yuan

et al. 2019

Sci. China Phys. Mech. Astron.

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In many closed quantum systems, an interesting phenomenon, called quantum carpet, can be observed, where the evolution of wave function exhibits a carpet-like pattern. The mechanism of quantum carpet is similar to the classical interference pattern of light. Although the origin of quantum carpets has been studied previously, there are still many interesting details worth exploring. Here, we presented a unified framework for a simultaneous analyzing on three features of quantum carpets, namely full revival, fractional revival and diagonal canal. For fractional revival, a complete formula is presented to explain its generation through "Gaussian sum theory", in which all the essential features, including the phases and amplitudes, of this phenomenon could be captured analytically. Moreover, we also revealed the relations between the interference terms of the diagonal canals and their geometric interpretations, providing a better understanding in the formation of diagonal canals.

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A graph with fractional revival

Cited by 20 publications

References 21 publications

Pretty good quantum fractional revival in paths and cycles

Pretty good quantum fractional revival in paths and cycles

Quantum walks on graphs of the ordered Hamming scheme and spin networks

Ordered space-time structures: Quantum carpets from Gaussian sum theory

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