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arXiv:2509.10100

Perfect pure quantum state transfer via state restoring and ancilla measurement

Edward B. Fel’dman, Jiun-Huei Proty Wu, Alexander Ivanovich Zenchuk

Published Sep 12, 2025• 0 citations
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Abstract

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 $k$-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 $S_0$, we encode this state into the $k$-excitation state of the sender, transfer and restore this state and finally decode the restored $k$-excitation state {of the receiver} into the state of another subsystem $R_0$. After labeling and removing the garbage via the ancilla-state measuring we complete the algorithm for the perfect transfer of an arbitrary pure state.

DOI
10.48550/arxiv.2509.10100

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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 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.
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.
Abstract We propose an algorithm to create an arbitrary n -qubit pure quantum superposition state with precision of m -decimals (binary representation) for each probability amplitude. The algorithm uses one-qubit rotations, Hadamard transformations and, C-NOT operations with multi-qubit controls. The depth of the circuit is O (2 n n ), its space is O ( n ). We emphasize that the parameters of the utilized unitary transformations are predicted in advance by the required precision and therefore there is no classical calculation supplementing this quantum algorithm. Finalizing the state-creation we perform the measurement of the ancilla state with a certain desired output with the purpose of removing all the garbage from the created superposition state. If n and m are independent and n ≫ m , the probability of access to the desired ancilla-state (success probability) is ~ 2 −n , which requires O (2 n ) runs of the algorithm and leads to the overall depth O (4 n n ). However, the situation can be significantly improved by replacing the usual measurement with the controlled measurement of the ancilla state that, first of all, removes the garbage part of the superposition state and, second (and most important), allows to avoid both the problem of small success probability to the desired ancilla state and multiple runs of the algorithm. As a consequence, the depth of the algorithm is O (2 n n ) in this case. If m serves to provide the required fidelity of state approximation, then the above parameters increase. This algorithm can be a subroutine generating the required input state in various algorithms, in particular, in matrix-manipulation algorithms developed earlier.
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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 is proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits.
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.