Perfect (s,r)-state transfer
Abstract
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 u = ea + s eb to μ=eα + r eβ, 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 u = ea + s eb to μ=eα + r eβ (up to some dilation) where r,s∈ ℂ. We identify infinite families of graphs with perfect (s,r)-state transfer and provide characterizations of cases when |r|= |s| and when |r|≠ |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 u. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect (s,r)-state transfer.
Related
- Quantum State Routing and Perfect State Transfer on Signed Graphs under Environmental Noise
- Perfect state transfer on Cayley graphs over dihedral groups: A complete and practical characterization
- Spectral width and polynomial degree in perfect state transfer
- Perfect state transfer on mixed graphs: complete classes and transfer times
- Perfect and peak state transfer on IBM quantum hardware
BibTeX
@misc{kirkland2026perfect,
title = {{Perfect $(s,r)$-state transfer}},
author = {Stephen Kirkland and Hermie Monterde and Sarah Plosker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10713},
eprint = {2609.10713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10713},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Perfect (s,r)-state transfer
AU - Stephen Kirkland
AU - Hermie Monterde
AU - Sarah Plosker
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10713
UR - https://arxiv.org/abs/2609.10713
AB - 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 u = e_a + s e_b to μ=e_α + r 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 u = e_a + s e_b to μ=e_α + r e_β (up to some dilation) where r,s∈ ℂ. We identify infinite families of graphs with perfect (s,r)-state transfer and provide characterizations of cases when |r|= |s| and when |r|≠ |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 u. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect (s,r)-state transfer.
ER -