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Transfer of scaled MQ-coherence matrices

G. A. Bochkin, Alexander Ivanovich Zenchuk

Published Dec 31, 2017• 0 citations
OpenAlex

Abstract

We show that quantum states of a certain structure can be transferred from the sender to the receiver without mixing the matrix elements. The only effect of such a state transfer is scaling { of the} certain blocks (MQ-coherence matrices) of the transferred matrix. In addition, equal scaling of these blocks is also possible. We consider the transfer of two-qubit states along a homogeneous spin-1/2 chain and find the states admitting perfect transfer of their zero-order coherence matrices.

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We show that quantum states of a certain structure can be transferred from the sender to the receiver without mixing the matrix elements. The only effect of such a state transfer is scaling { of the} certain blocks (MQ-coherence matrices) of the transferred matrix. In addition, equal scaling of these blocks is also possible. We consider the transfer of two-qubit states along a homogeneous spin-1/2 chain and find the states admitting perfect transfer of their zero-order coherence matrices.
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.
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].
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.
Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with homogeneous interactions. These restrictions allow finding numerous examples of systems that show perfect transfer but in geometries that are not implementable or are very difficult to implement in actual experimental settings. Relaxing the homogeneity of the interactions and inspired by the XXXXXX qubit chains that show perfect transmission, we present a simple scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission. We present some simple examples and show how it is possible to generalize them for longer transmission lengths.
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.
In this work, quantum correlations in two model systems which can be invesitgated by means of solid-state NMR are considered. The first is a two-spin system in NMR spin-locking experiment, where two schemes of spin-locking are considered. Concurrence is calculated for both schemes assuming the initial thermodynamic equilibrium state. Quantum discord is calculated analytically in the high-temperature approximation. The second model system is the spin-1/2 chain with the XY interaction, where the transfer of multiple quantum (MQ) coherences from one end of the chain to another is studied. The conditions under which the density matrix of the receiver is a block-scaled version of the sender’s density matrix are found.