Quantum perfect state transfer on weighted join graphs

Ricardo Javier Angeles-Canul; Rachael M. Norton; Michael C. Opperman; Christopher C. Paribello; Matthew C. Russell; Christino Tamon

doi:10.1142/S0219749909006103

Quantum perfect state transfer on weighted join graphs

Ricardo Javier Angeles-Canul, Rachael M. Norton, Michael C. Opperman, Christopher C. Paribello, Matthew C. Russell, Christino Tamon^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. ¹ where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.² and Moore and Russell.³

Original language	English (US)
Pages (from-to)	1429-1445
Number of pages	17
Journal	International Journal of Quantum Information
Volume	7
Issue number	8
DOIs	https://doi.org/10.1142/S0219749909006103
State	Published - Dec 2009

Funding

This research was supported by the National Science Foundation grant DMS-0646847 and the National Security Agency grant H98230-09-1-0098.

Keywords

Join
Perfect state transfer
Quantum networks
Weighted graphs

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1142/S0219749909006103

Cite this

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title = "Quantum perfect state transfer on weighted join graphs",

abstract = "This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. 1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3",

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author = "Angeles-Canul, {Ricardo Javier} and Norton, {Rachael M.} and Opperman, {Michael C.} and Paribello, {Christopher C.} and Russell, {Matthew C.} and Christino Tamon",

note = "Funding Information: This research was supported by the National Science Foundation grant DMS-0646847 and the National Security Agency grant H98230-09-1-0098.",

year = "2009",

month = dec,

doi = "10.1142/S0219749909006103",

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AU - Norton, Rachael M.

AU - Opperman, Michael C.

AU - Paribello, Christopher C.

AU - Russell, Matthew C.

AU - Tamon, Christino

N1 - Funding Information: This research was supported by the National Science Foundation grant DMS-0646847 and the National Security Agency grant H98230-09-1-0098.

PY - 2009/12

Y1 - 2009/12

N2 - This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. 1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3

AB - This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. 1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3

KW - Join

KW - Perfect state transfer

KW - Quantum networks

KW - Weighted graphs

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Quantum perfect state transfer on weighted join graphs

Abstract

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Keywords

ASJC Scopus subject areas

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