Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0604137 · Physical Review Letters

Unifying Quantum State Transfer and State Amplification

Alastair Kay

Published Jan 4, 2007• 75 citations
arXivHTMLPDF

Abstract

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.

DOI
10.1103/physrevlett.98.010501

Related papers

PERFECT, EFFICIENT, STATE TRANSFER AND ITS APPLICATION AS A CONSTRUCTIVE TOOL

Alastair Kay

We review the subject of perfect state transfer — how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

arXiv:0903.4274•International Journal of Quantum Information•Jun 1, 2010•320 citations

Quantum state transfer through noisy quantum cellular automata

Avalle, M, Genoni, MG, Alessio Serafini

We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy quantum cellular automata in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.

•May 15, 2015•6 citations

Quantum state transfer through noisy quantum cellular automata

Michele Avalle, Marco G. Genoni, Alessio Serafini

We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata (QCA) evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy QCA in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.

arXiv:1411.0936•Journal of Physics A Mathematical and Theoretical•Apr 22, 2015•3 citations

Perfect and Pretty Good State Transfer for Field-Free Heisenberg Chains

Alastair Kay

In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In attempting to engineer arbitrarily accurate transfer, where explore a new paradigm that facilitates time estimates for achieving any target accuracy $\epsilon$ for the transfer.

•Jun 14, 2019•1 citation

Identifying quantum states capable of high-fidelity transmission over a spin chain

Zhao-Ming Wang, Lian-Ao Wu, C. Allen Bishop +2 more

A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.

arXiv:1210.6550•Physical Review A•Sep 4, 2013•3 citations

Quantum communication and state transfer in spin chains

Joris Van Der Jeugt

We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q -hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q -Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation.

Journal of Physics Conference Series•Mar 1, 2011•3 citations
We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.
We review the subject of perfect state transfer — how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.
We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy quantum cellular automata in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.
We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata (QCA) evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy QCA in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.
In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In attempting to engineer arbitrarily accurate transfer, where explore a new paradigm that facilitates time estimates for achieving any target accuracy ϵ\epsilonϵ for the transfer.
A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.
We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q -hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q -Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation.