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arXiv:quant-ph/0506156 · Physical Review A

Quantum-state transfer characterized by mode entanglement

Xiao‐Feng Qian, Ying Li, Yong Li, Z. Song, C. P. Sun

Published Dec 30, 2005• 30 citations
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Abstract

We study the quantum-state transfer (QST) of a class of tight-bonding Bloch electron systems with mirror symmetry by considering the mode entanglement. Some rigorous results are obtained to reveal the intrinsic relationship between the fidelity of QST and the mirror mode concurrence (MMC), which is defined to measure the mode entanglement with a certain spatial symmetry and is just the overlap of a proper wave function with its mirror image. A complementarity is discovered as the maximum fidelity is accompanied by a minimum of the MMC. At the instant that is just half of the characteristic time required to accomplish a perfect QST, the MMC can reach its maximum value of 1. A large class of perfect QST models with a certain spectral structure is discovered to support our analytical results.

DOI
10.1103/physreva.72.062329

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The quantum state transmission through the medium of high-dimensional many-particle system (boson or spinless fermion) is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor (NN). We also study a simple but realistic near half-filled tight-binding fermion system with uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.
Reliably transferring a quantum state from one location to another, as well as generating entangled states, are important tasks to achieve in quantum spin systems. The fidelity or probability of state transfer is a number between 0 and 1 that measures the closeness of two quantum states. Fidelity is used to determine the accuracy of quantum state transfer. There are several interesting phenomena of quantum state transfer defined via fidelity: perfect state transfer, pretty good state transfer, and fractional revival. This thesis contains results about the perfect state transfer property of some special classes of graphs, including Hadamard diagonalizable graphs, weighted paths with loops, as well as switched and partially switched hypercubes. A correspondence between the class of graphs that are diagonalizable by a standard Hadamard matrix and the class of cubelike graphs is given. Sensitivity of fidelity to errors when perfect state transfer occurs is analysed: if a system admits perfect state transfer at some time t, bounds on fidelity of state transfer at t+h for very small h are given, as well as bounds on fidelity of a slightly perturbed system at time t. Finally, Laplacian fractional revival on graphs is considered; in particular the thesis contains a characterization of threshold graphs that admit Laplacian fractional revival.
We show that a perfect quantum-state transmission can be realized through a spin chain possessing the commensurate structure of an energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry discovered by Albanese et al. (e-print quant-ph∕0405029), the parity matched commensurability of the energy spectra helps us to present preengineered spin systems for quantum information transmission. Based on these theoretical analyses, we propose a protocol of near-perfect quantum-state transfer by using a ferromagnetic Heisenberg chain with uniform coupling constant, but an external parabolic magnetic field. The numerical results show that the initial Gaussian wave packet in this system with optimal field distribution can be reshaped near perfectly over a longer distance.
Abstract Continuous U(1) gauge symmetry, which guarantees the conservation of total excitations in linear bosonic systems, will be broken when it comes to the strong-coupling regime where the rotation wave approximation (RWA) fails. Here we develop analytic solutions for multi-mode bosonic systems with XX-type couplings beyond RWA, and propose a novel scheme to implement high-fidelity quantum state transfer (QST) and entanglement preparation (EP) with high speed. The scheme can be realized with designated coupling strength and pulse duration with which the excitation number keeps unchanged regardless of the breakdown of the global U(1) symmetry. In QST tasks, we consider several typical quantum states and demonstrate that this method is robust against thermal noise and imperfections of experimental sequence. In EP tasks, the scheme is successfully implemented for the preparation of Bell states and W-type states, within a shortest preparation time.