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Russian Microelectronics

Quantum Coherence Restoring in Communication Line via Strong Pulse-Form Interaction with Environment

Edward B. Fel’dman, I. D. Lazarev, Alexander Nikolaevich Pechen, Alexander Ivanovich Zenchuk

Published Dec 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1063739725601201

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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 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.
We consider the multi-qubit fixed-excitation state transfer along the spin chain with dipole-dipole interaction subjected to the interaction with environment governed by the Lindblad equation preserving the excitation number during spin-evolution. The state transfer algorithm includes the state restoring via Kraus operators and ancilla measurement. As a result, the transferred state appears in superposition with completely mixed state, the latter disappears with vanishing interaction with environment. In that case we deal with probabilistic perfect state transfer. Example of an arbitrary multi-qubit one-excitation state transfer is present and its robustness with respect to perturbation of the Kraus operators is studied.
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 consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length.
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.
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.