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arXiv:2504.15832 · International Journal of Quantum Information

Restoring of quantum state transferred along XY-spin chain and entanglement evolution

N. A. Tashkeev, Alexander Ivanovich Zenchuk

Published Apr 10, 2025• 0 citations
arXivHTMLPDF

Abstract

We propose a protocol restoring the state transferred along the spin chain governed by the XY-Hamiltonian. Such dynamics does not preserve the excitation number and leads to mixing multiple-quantum coherence matrices of orders having the same parities. Depending on the initial state, this results in generating either all possible or only even-order multiple-quantum coherence matrices. Restoring is established via the special unitary transformation applied to the receiver side of the chain (extended receiver). An example of restoring [Formula: see text]- and [Formula: see text]-order coherence matrices in two-qubit state transfer is considered. Entanglement transfer in such process is also studied and possibility of its amplification is demonstrated.

DOI
10.1142/s021974992550011x

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We propose a protocol restoring the state transferred along the spin chain governed by the XY-Hamiltonian. Such dynamics does not preserve the excitation number and leads to mixing multiple-quantum coherence matrices of orders having the same parities. Depending on the initial state, this results in generating either all possible or only even-order multiple-quantum coherence matrices. Restoring is established via the special unitary transformation applied to the receiver side of the chain (extended receiver). An example of restoring [Formula: see text]- and [Formula: see text]-order coherence matrices in two-qubit state transfer is considered. Entanglement transfer in such process is also studied and possibility of its amplification is demonstrated.
The evolution of quantum coherences comes with a set of conservation laws provided that the Hamiltonian governing this evolution conserves the spin-excitation number. At that, coherences do not intertwist during the evolution. Using the transmission line and the receiver in the initial ground state we can transfer the coherences to the receiver without interaction between them, although the matrix elements contributing to each particular coherence intertwist in the receiver’s state. Therefore we propose a tool based on the unitary transformation at the receiver side to untwist these elements and thus restore (at least partially) the structure of the sender’s initial density matrix. A communication line with two-qubit sender and receiver is considered as an example of implementation of this technique.
Abstract We propose a protocol for restoring states transferred along a spin-1/2 chain utilizing a controlled interaction of the spin-chain with the environment. Such interaction exploits an incoherent quantum control and is described by the master equation with Lindblad operators having time-dependent pulse-sequence form. The amplitudes of the pulses are properly adjusted to perform the state restoring. We apply this protocol to restore the 1-order coherence matrix of the (0,1)-excitation of a 2-qubit state transferred along the spin-1/2 chain governed by the XXZ-Hamiltonian preserving the excitation number in the system.
We study the long distance [Formula: see text]-excitation state restoring in the linear open chain governed by the XX-Hamiltonian. We show that restoring the 1-order coherence matrix results in restoring the 1-excitation block of the 0-order coherence matrix, so that only one 0-excitation element of the density matrix remains unrestored. Such restoring also scales the concurrence between any two qubits of the transferred state, the scaling factor is defined by the Hamiltonian and doesn’t depend on the initial sender’s state. Sender–Receiver entanglement is also studied via the PPT criterion.
In the present work the generation of entanglement between the receiver and sender is investigated in the process of the quantum state transfer in the homogeneous one-dimensional chain of spins 1/2 with the XY -Hamiltonian in the approximation of the nearest neighbour interactions. Fidelity is obtained for a quantum state transfer for various numbers of spins and temperatures and values of initial polarisation of the sender’s spin. The transmitted pure state is encoded in the state of first spin (sender) in the initial time moment. The other spins are in the thermodynamic equilibrium state. The reduced density matrix for the receiver and the sender is obtained for an investigation of entanglement in the “sender-receiver” system. The effect of temperature and polarization of the transmitted state on the generation of entanglement in the system is also investigated.
We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem can be proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits. We show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a time scale of the order of [Formula: see text].
We propose the protocol for perfect state transfer of an arbitrary pure quantum state along the spin-1/2 chain governed by the Hamiltonian preserving the excitation number in the system. We show that the kkk-excitation pure sender's state can be restored at the receiver using only the local transformations over the qubits of the extended receiver. The restored state appears in the superposition with other states which form garbage. This garbage can be easily removed by including the ancilla, whose state labels the garbage, and then measuring the {ancilla state} with desired output. The resulting state of the receiver coincides with the initial sender's state {up to the unimportant common phase factor.} Then, to transfer an arbitrary {pure} state of some system S0S_0S0​, we encode this state into the kkk-excitation state of the sender, transfer and restore this state and finally decode the restored kkk-excitation state {of the receiver} into the state of another subsystem R0R_0R0​. After labeling and removing the garbage via the ancilla-state measuring we complete the algorithm for the perfect transfer of an arbitrary pure state.