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arXiv:1502.02458 · Physical Review A

Transfer of arbitrary two-qubit states via a spin chain

Salvatore Lorenzo, Tony J. G. Apollaro, Simone Paganelli, G. Massimo Palma, Francesco Plastina

Published Apr 16, 2015• 56 citations
arXivHTMLPDF

Abstract

We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-$\frac{1}{2}$ 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 $XX$-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.

DOI
10.1103/physreva.91.042321

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The transfer of an unknown quantum state, from a sender to a receiver, is one of the main requirements to perform quantum information processing (QIP) tasks. In this respect, the state transfer of a single qubit by means of spin chains has been widely discussed, and many protocols aiming at performing this task have been proposed. Nevertheless, the state transfer of more than one qubit has not been properly addressed so far. In this paper, we present a modified version of a recently proposed quantum state transfer (QST) protocol (Lorenzo S, Apollaro T J G, Sindona A and Plastina F 2013 Phys. Rev. A 87 042313 ) to obtain a quantum channel for the transfer of two qubits. This goal is achieved by exploiting Rabi-like oscillations due to excitations induced by means of strong and localized magnetic fields. We derive exact analytical formulae for the fidelity of the QST and obtain a high-quality transfer for general quantum states as well as for specific classes of states relevant for QIP.
We consider an unmodulated linear spin chain composed of two qubits at the ends, which undergo nearest-neighbor interactions, with an arbitrary spin between them. The state of the qubit on one end is to be transmitted through the arbitrary spin and is received by the qubit on the other end with some fidelity. We look at the behavior of the average f idelity of state transfer through time as affected by the spin quantum number of the arbitrary spin in between the qubits. We f ind that the higher the spin quantum number becomes, the earlier it takes to achieve perfect or nearly perfect state transfer. Moreover, when the channel with arbitrary spin is subjected to environment interaction, results from the calculation of average fidelity suggest that increasing the spin quantum number of the channel provides a countermeasure to the effects of decoherence induced by the environment.
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].
Quantum state transfer along a one-dimensional spin chain has become a fundamental ingredient for quantum communication between distant nodes in a quantum network. We study the average fidelity of quantum state transfer (QST) along an XYXYXY spin chain by adjusting the basis identification between the first spin and the last spin. In a proper choice of the basis identification, we find that the QST fidelity depends only on the average parity of the initial state linearly. We propose a simple scheme to adjust the basis identification to optimize the average fidelity such that it depends linearly on the absolute value of the average parity. In the case where the absolute value of the average parity is 1 we prove that the fidelity takes the maximum at any time over arbitrary initial state and basis identification.
We consider the transfer of an arbitrary qubit state through a linear spin chain for N=4, 5, and 6 spins, each with a spin-S channel. We calculate the average fidelity between the arbitrary initial state of the qubit at one end and the time evolved qubit state at the opposite end of the chain. We show that increasing the quantum number S of the channel spins allows attaining near perfect state transfer at an earlier time for the isotropic exchange case. We also show that an opposite effect is observed in the anisotropic case.
Abstract The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of three and four interacting qubits.