Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary $d$ -level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer, $d$ -level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.YnFollowing the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary $d$-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer, $d$-level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.Yn

arXiv:0803.2334Journal of Physics A Mathematical and TheoreticalOct 20, 200816 citations

Perfect $(s,r)$ -state transferPerfect $(s,r)$-state transfer

Stephen Kirkland, Hermie Monterde, Sarah Plosker

Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirected graph, and studying vertex-to-vertex dynamics. This setup has recently been relaxed to allow for dynamics between linear combinations of two vertex states, i.e.\ from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$ , where $r=s$ is either $-1$ (which corresponds to pair state transfer) or $+1$ (which corresponds to plus state transfer), or more recently $r=s$ is taken to be any real number (which corresponds to $s$ -pair state transfer). Here, we broaden the investigation of $s$ -pair state transfer to \textit{perfect $(s,r)$ -state transfer}, which is perfect state transfer from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$ (up to some dilation) where $r,s\in \mathbb C$ . We identify infinite families of graphs with perfect $(s,r)$ -state transfer and provide characterizations of cases when $|r|= |s|$ and when $|r|\neq |s|$ , showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time $t$ starting from a given $s$ -pair state $\mathbf u$ . Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect $(s,r)$ -state transfer.Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirected graph, and studying vertex-to-vertex dynamics. This setup has recently been relaxed to allow for dynamics between linear combinations of two vertex states, i.e.\ from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$, where $r=s$ is either $-1$ (which corresponds to pair state transfer) or $+1$ (which corresponds to plus state transfer), or more recently $r=s$ is taken to be any real number (which corresponds to $s$-pair state transfer). Here, we broaden the investigation of $s$-pair state transfer to \textit{perfect $(s,r)$-state transfer}, which is perfect state transfer from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$ (up to some dilation) where $r,s\in \mathbb C$. We identify infinite families of graphs with perfect $(s,r)$-state transfer and provide characterizations of cases when $|r|= |s|$ and when $|r|\neq |s|$, showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time $t$ starting from a given $s$-pair state $\mathbf u$. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect $(s,r)$-state transfer.

quant-pharXiv:2609.10713Sep 11, 20260 citations

Quantum-state transfer in imperfect artificial spin networks (6 pages)

Mauro Paternostro

Physical Review AJan 1, 20050 citations

Perfect mixed state quantum transport in correlated spin networks

Ashok Ajoy, Paola Cappellaro

Bulletin of the American Physical SocietyFeb 28, 20120 citations

Explicit designs of spin chains for perfect quantum state transfer

X. Q. Xi, Jiangbin Gong, T. Zhang +2 more

The European Physical Journal DOct 24, 20089 citations

Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary

d

-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer,

d

-level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.Yn

Perfect

(s,r)

-state transfer

\mathbf u = \mathbf e_a + s \mathbf e_b

\mathbf μ=\mathbf e_α + r \mathbf e_β

, where

r=s

is either

-1

(which corresponds to pair state transfer) or

+1

(which corresponds to plus state transfer), or more recently

r=s

is taken to be any real number (which corresponds to

s

-pair state transfer). Here, we broaden the investigation of

s

-pair state transfer to \textit{perfect

(s,r)

-state transfer}, which is perfect state transfer from

\mathbf u = \mathbf e_a + s \mathbf e_b

\mathbf μ=\mathbf e_α + r \mathbf e_β

(up to some dilation) where

r,s\in \mathbb C

. We identify infinite families of graphs with perfect

(s,r)

-state transfer and provide characterizations of cases when

|r|= |s|

and when

|r|\neq |s|

, showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time

t

starting from a given

s

-pair state

\mathbf u

. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect

(s,r)

-state transfer.