Controlled quantum state transfer in XX spin chains at the Quantum Speed Limit

Coden, Diego S. Acosta; Gómez, Sergio S.; Ferrón, Alejandro; Osenda, Omar

doi:10.1016/j.physleta.2020.127009

Cited by 15 publications

(11 citation statements)

References 49 publications

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“…Obtaining analytical expressions in a completely general scenario would be impossible. We start asking for centrosymmetric spin chains as in most of our previous works [34,54,55]…”

Section: Exact Solution For Spin Chains With Staggered Exchange Coupl...mentioning

confidence: 99%

“…On the other hand, much progress have been made concerning the non-autonomous time evolution of spin chains [29][30][31][32][33][34], although many times the control leads to particular results about the times for which the transfer is achievable [29][30][31][32][33]. The controllability of the dynamics is a well studied area with numerous results [29,[35][36][37].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

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We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two diﬀerent values. We work out the exact solutions in the one- excitation sub-space. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

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“…Obtaining analytical expressions in a completely general scenario would be impossible. We start asking for centrosymmetric spin chains as in most of our previous works [34,54,55]…”

Section: Exact Solution For Spin Chains With Staggered Exchange Coupl...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…While an extensive analysis of the performance of our protocol under these conditions has not been presented here, and may be left to future investigation, it is reasonable to assume that similar analyses done for the one-particle transfer scenario may apply also for two-particle routing as our results are derived from single-particle transition amplitudes. In this regard, disorder in couplings [ 21 , 30 , 31 , 32 , 33 ], time-dependent couplings [ 34 , 35 ], and decoherence [ 36 , 37 ] have been extensively addressed and several strategies to counter the detrimental effect on the transfer quality have been devised which may find application also in our two-particle routing protocol.…”

Section: Discussionmentioning

confidence: 99%

Two-Excitation Routing via Linear Quantum Channels

Apollaro

Chetcuti

2020

Entropy

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Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on a recently proposed many-excitation transfer protocol, we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protocol allows for efficient two-excitation routing on a fermionic network, although for a spin-12 network only a limited region of the network is suitable for high-quality routing.

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“…Obtaining analytical expressions in a completely general scenario would be impossible. We start asking for centrosymmetric spin chains as in most of our previous works [34,40,41]…”

Section: Exact Solution For Spin Chains With Staggered Exchange Coupl...mentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra,

Ferrón,

Osenda

2022

Preprint

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We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. We work out the exact solutions in the one-excitation subspace. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

show abstract

Controlled quantum state transfer in XX spin chains at the Quantum Speed Limit

Cited by 15 publications

References 49 publications

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Two-Excitation Routing via Linear Quantum Channels

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

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