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.
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.
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.
Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following: turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. We also propose a protocol for solving a system of linear algebraic equations with a system of two equations as an example. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.
We combine the long-distance quantum state transfer and simple operations with the elements of the transferred (nor perfectly) density matrix. These operations are turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. The basic tool performing these operations is the unitary transformation on the extended receiver. A system of linear algebraic equations can be solved in this way as well. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.
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 discuss restrictions imposed by quantum mechanics on the process of matrix elements transfer from the one system to another. This is relevant for various processes of partial state transfer (quantum communication, indirect measurement, polarization transfer, {\it etc}). Given two systems A and B with initial density operators λ and r, respectively, we consider most general interactions, which lead to transferring certain matrix elements of unknown λ into those of the final state r of B. We find that this process leads to eliminating the memory on the transferred (or certain other) matrix elements from the final state of A. If one diagonal matrix element is transferred: raa=λaa, the memory on each non-diagonal element λa=b is completely eliminated from the final density operator of A. The transfer of a non-diagonal element: rab=λab eliminates the memory on the diagonal elements λaa and λbb, while the memory about their sum λaa+λbb is kept. Moreover, the memory about λab itself is completely eliminated from the final state of A. Generalization of these set-ups to non-ideal transfer brings in a trade-off between the quality of the transfer and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations.