Quantum transfer of interacting qubits

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 3 and 4 interacting qubits.

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

“…Beyond the difficulties presented by the Heisenberg model and the QST of arbitrary onequbit states, there is a bonanza de new proposals. Among these novel propositions are the transfer of multilevel states [19,[40][41][42][43][44][45][46], also called d-levels states, transfer protocols dealing with multiple qubit states [47][48][49][50], perfect transfer in graphs or two-or three-dimensional settings [9,51,52], and the transfer of several quantum states in parallel using only a single channel [53]. The works dealing with these ideas are both theoretical and experimental.…”

Understanding the propagation of excitations in quantum spin chains with different kind of interactions

“…So, at least for small values of n, the computing time demanded by the diagonalizations would not render the algorithm useless. For instance, the trasmission protocol employed by Appollaro and collaborators [53,54] to transmit more than one qubit would increase the number of parameters to optimize by just a pair more than the number involved in the problem with a single excitation.…”

Long distance entanglement and high-dimensional quantum teleportation in the Fermi–Hubbard model

“…Therefore, the creation and distribution of entanglement in physical platforms is crucial in the success and implementation of quantum teleportation protocols 7 . In this context, a variety of one-dimensional quantum spin chains are known for their entangled ground states and have been intensively investigated as faithful architectures for quantum information processing [8][9][10][11][12][13][14][15] and notably as reliable quantum channels for teleportation protocols [16][17][18][19][20][21][22][23][24][25][26] . Nevertheless, in most one-dimensional quantum spin chain systems with short-range interactions, the entanglement vanishes for distances larger than two neighboring sites [27][28][29] , which makes them inconceivable platforms for long distance teleportation.…”