Spin Chains as Perfect Quantum State Mirrors

Abstract

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.

Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications)

References in corpus (15)

• Quantum Communication Through an Unmodulated Spin Chain
• Perfect state transfer in quantum spin networks
• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Dynamics of Entanglement in One-Dimensional Spin Systems
• Mirror Inversion of Quantum States in Linear Registers
• Conclusive and arbitrarily perfect quantum state transfer using parallel spin chain channels
• The Propagation of Quantum Information Through a Spin System
• Entanglement dynamics and quantum state transport in spin chains
• Perfect State Transfer, Effective Gates and Entanglement Generation in Engineered Bosonic and Fermionic Networks
• Quantum state transfer via the ferromagnetic chain in a spatially modulated field
• Perfect quantum state transfer with randomly coupled quantum chains
• From perfect to fractal transmission in spin chains
• Solid-State Quantum Communication With Josephson Arrays
• Efficient and perfect state transfer in quantum chains
• Quantum state transfer in imperfect artificial spin networks

Cited by in corpus (147)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• A Review of Perfect State Transfer and its Application as a Constructive Tool
• Robust Quantum State Transfer in Random Unpolarized Spin Chains
• Colloquium: Atomic spin chains on surfaces
• Perfect state transfer on a spin-chain without state initialization
• Perfect State Transfer: Beyond Nearest-Neighbor Couplings
• Quantum Speed Limit for Perfect State Transfer in One Dimension
• Perfect state transfer in long-range interacting spin chains
• How to construct spin chains with perfect state transfer
• 99%-fidelity ballistic quantum-state transfer through long uniform channels
• Long quantum channels for high-quality entanglement transfer
• Robustness of spin-coupling distributions for perfect quantum state transfer
• Perfect Quantum Routing in Regular Spin Networks
• Quantum-state transfer via resonant tunnelling through local field induced barriers
• Improved transfer of quantum information using a local memory
• The Basics of Perfect Communication through Quantum Networks
• State Transfer and Spin Measurement
• Perfect state transfer in networks of arbitrary topology and coupling configuration
• Optimal quantum chain communication by end gates
• Quantum Impurity Entanglement
• Spin chains for robust state transfer: Modified boundary couplings vs. completely engineered chains
• Transfer of arbitrary two qubit states via a spin chain
• High-dimensional quantum state transfer through a quantum spin chain
• Fast, high fidelity information transmission through spin chain quantum wires
• Optimized dynamical control of state transfer through noisy spin chains
• Quantum state transfer and time-dependent disorder in Quantum Chains
• Local control of entanglement in a spin chain
• Adiabatic Quantum Transport in a Spin Chain with a Moving Potential
• Quantum communication beyond the localization length in disordered spin chains
• Quantum Logic between Remote Quantum Registers
• Exploiting boundary states of imperfect spin chains for high-fidelity state transfer
• Quantum state transfer in spin chains via shortcuts to adiabaticity
• Perfect function transfer and interference effects in interacting boson lattices
• Engineering correlation and entanglement dynamics in spin systems
• Transport of Quantum Correlations across a spin chain
• Use of dynamical coupling for improved quantum state transfer
• Entanglement localization by a single defect in a spin chain
• Quantum Information Processing with Delocalized Qubits under Global Control
• Universal Existence of Exact Quantum State Transmissions in Interacting Media
• Quantum communication through a spin chain with interaction determined by a Jacobi matrix
• Effect of perturbations on information transfer in spin chains
• Perfect state transfers by selective quantum interferences within complex spin networks
• Pretty good state transfer of entangled states through quantum spin chains
• A Processor Core Model for Quantum Computing
• All Possible Coupling Schemes in XY Spin Chains for Perfect State Transfer
• Quantum State Transfer Characterized by Mode Entanglement
• Iterative quantum state transfer along a chain of nuclear spin qubits
• Freezing distributed entanglement in spin chains
• Perfect quantum state transfer on diamond fractal graphs
• Speedup of quantum state transfer by three- qubit interactions: Implementation by nuclear magnetic resonance
• High probability state transfer in spin-1/2 chains: Analytical and numerical approaches
• Information-flux approach to multiple-spin dynamics
• The Non-Equilibrium Reliability of Quantum Memories
• Coherent ground-state transport of neutral atoms
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
• Quantum Error Correction for State Transfer in Noisy Spin Chains
• Fractional revivals of quantum state in tight-binding chain
• Variance squeezing and entanglement of the XX central spin model
• The high probability state transfers and entanglements between different nodes of the homogeneous spin 1/2 chain in inhomogeneous external magnetic field
• Simulation of mirror inversion of quantum states in an XY spin chain using NMR
• Advantages and limitations of quantum routing
• The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors
• Entanglement generation and perfect state transfer in ferromagnetic qubit chains
• Complete structural restoring of transferred multi-qubit quantum state
• Communication in quantum networks of logical bus topology
• Decoherence as attenuation of mesoscopic echoes in a spin-chain channel
• Almost perfect transport of an entangled two-qubit state through a spin chain
• An Exactly Solvable Spin Chain Related to Hahn Polynomials
• High-probability quantum state transfer among nodes of an open XXZ spin chain
• Mixed-state quantum transport in correlated spin networks
• Remote creation of a one-qubit mixed state through a short homogeneous spin-1/2 chain
• Evolutionary computation for adaptive quantum device design
• Information propagation in a quantum system. Examples of open spin-1/2 chains
• Relationship between probabilities of the state transfers and entanglements in spin systems with simple geometrical configurations
• Vibrational exciton-mediated quantum state transfert: a simple model
• Generating Quantum States through Spin Chain Dynamics
• Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of Quantum State Transfer
• Quantum state transfer in spin chains with q-deformed interaction terms
• Entanglement of Solitons in the Frenkel-Kontorova Model
• Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
• Combatting the Effects of Disorder in Quantum State Transfer
• Steady many-body entanglements in dissipative systems
• Quantum correlations in different density matrix representations of spin-1/2 open chain
• Perfect transfer of multiple excitations in quantum networks
• Almost perfect transmission of multipartite entanglement through disordered and noisy spin chains
• Learning Effective Spin Hamiltonian of Quantum Magnet
• Quantum state swapping via qubit network with Hubbard interaction
• Photon-assisted quantum state transfer and entanglement generation in spin chains
• Determinant representations of spin-operator matrix elements in the XX spin chain and their applications
• Knitting distributed cluster state ladders with spin chains
• Quantum state transfer with untuneable couplings
• Transfer of 0-order coherence matrix along spin-1/2 chain
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Exact Fractional Revival in Spin Chains
• Robustness of spin-chain state-transfer schemes
• Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder
• Time-crystalline behavior in an engineered spin chain
• Partial structural restoring of two-qubit transferred state
• Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains
• Graph state generation with noisy mirror-inverting spin chains
• Robust and efficient transport of two-qubit entanglement via disordered spin chains
• Transport in deformed centrosymmetric networks
• Remote two-qubit state creation and its robustness
• Tailoring Spin Chain Dynamics for Fractional Revivals
• W-like states of N uncoupled spins 1/2
• Information transfer rates in spin quantum channels
• Dipole-phonon quantum logic with alkaline-earth monoxide and monosulfide cations
• Pretty good state transfer via adaptive quantum error correction
• Quantum Complexity: restrictions on algorithms and architectures
• Transferring entangled states through spin chains by boundary-state multiplets
• Optimal remote restoring of quantum states in communication lines via local magnetic field
• Parity-dependent state transfer for direct entanglement generation
• A New Method for Multi-Bit and Qudit Transfer Based on Commensurate Waveguide Arrays
• Temperature-dependent remote control of polarization and coherence intensity with pure sender's initial state
• Newton's cradle analogue with Bose-Einstein condensates
• Co-Processors for Quantum Devices
• Nearly optimal time-independent reversal of a spin chain
• Noise effects in perfect transmission of quantum states
• Quantum Corralling
• Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing
• Quantum-state transfer on spin-chain channels with random imperfection
• Perfect State Transfer in a Spin Chain without Mirror Symmetry
• Quasi-Perfect State Transfer in Spin Chains via Parametrization of On-Site Energies
• High-fidelity state transfer via quantum walks from delocalized states
• Effects of impurity on fidelity of quantum state transfer via spin channels
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• M-neighbor approximation in one-qubit state transfer along zigzag and alternating spin-1/2 chains
• Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian
• Tuning and Amplifying the Interactions in Superconducting Quantum Circuits with Subradiant Qubits
• Remote control of quantum correlations in two-qubit receiver via three-qubit sender
• Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian
• Spin and electronic excitations in $4f$ atomic chains on Au(111) substrates
• Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models
• Scalable Quantum Spin Networks from Unitary Construction
• Perfect transfer of arbitrary continuous variable states across optical waveguide lattices
• Creating and preserving multi-partite entanglement with spin chains
• Quantum correlations between distant qubits conveyed by large-$S$ spin chains
• One-excitation spin dynamics in homogeneous closed chain governed by XX-Hamiltonian
• Large effects of boundaries on spin amplification in spin chains
• Realization of Surface Code Quantum Memory on Systems with Always-On Interactions
• Incorporating Encoding into Quantum System Design
• Expediting quantum state transfer through the long-range extended XY model
• State transfer analysis for linear spin chains with non-uniform on-site energies
• Coherence restoring in communication line via controlled interaction with environment
• Teleportation via spin-1/2 chain in solid-state quantum architecture
• Emergent mirror symmetry in the optimization of the central-spin quantum battery
• Effect of Emitters on Quantum State Transfer in Coupled Cavity Arrays