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arXiv:0806.4568 · Physical Review A

Exploiting quench dynamics in spin chains for distant entanglement and quantum communication

Hannu Christian Wichterich, Sougato Bose

Published Jun 4, 2009• 49 citations
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Abstract

We suggest a method of entangling significantly the distant ends of a spin chain using minimal control. This entanglement between distant individual spins is brought about solely by exploiting the dynamics of an initial mixed state with N\'eel order if the lattice features nearest-neighbor $XXZ$ interaction. There is no need to control single spins or to have engineered couplings or to pulse globally. The method only requires an initial nonadiabatic switch (a quench) between two Hamiltonians followed by an evolution under the second Hamiltonian. The scheme is robust to randomness of the couplings as well as the finiteness of an appropriate quench and could potentially be implemented in various experimental setups, ranging from atoms in optical lattices to Josephson-junction arrays.

DOI
10.1103/physreva.79.060302

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We suggest a method of entangling significantly the distant ends of a spin chain using minimal control. This entanglement between distant individual spins is brought about solely by exploiting the dynamics of an initial mixed state with N'eel order if the lattice features nearest-neighbor XXZXXZXXZ interaction. There is no need to control single spins or to have engineered couplings or to pulse globally. The method only requires an initial nonadiabatic switch (a quench) between two Hamiltonians followed by an evolution under the second Hamiltonian. The scheme is robust to randomness of the couplings as well as the finiteness of an appropriate quench and could potentially be implemented in various experimental setups, ranging from atoms in optical lattices to Josephson-junction arrays.
We study the problem of entangling two spins at the distant ends of a spin chain by exploiting the nonequilibrium dynamics of the system after a sudden global quench. As initial states we consider a canted or spiral order product state of the spins and singlets of neighboring pairs of spins. We find that within the class of canted order initial states, no entanglement is generated at any time except for the special case of the N\'eel state. While an earlier work has shown that the N\'eel state is indeed an excellent starting resource for the dynamical generation of long-distance entanglement, the curious fact that this is the sole point within a large class of initial product states of the spins was not noted. On the other hand, we find that an initial state which is a series of nearest-neighbor Bell states, and well motivated by some physical realizations, is also a good starting resource for end to end entanglement in a way similar to that of the N\'eel state. The scheme is shown to be robust to random single spin flip in the initial N\'eel state as well as to randomness of the couplings.
We optimize a quantum walk of multiple fermions following a quench in a spin chain to generate near-ideal resources for quantum networking. We first prove a useful theorem mapping the correlations evolved from specific quenches to the apparently unrelated problem of quantum state transfer between distinct spins. This mapping is then exploited to optimize the dynamics and produce large amounts of entanglement distributed in very special ways. Two applications are considered: the simultaneous generation of many Bell states between pairs of distant spins (maximal block entropy) and high entanglement between the ends of an arbitrarily long chain (distance-independent entanglement). Thanks to the generality of the result, we study its implementation in different experimental setups using present technology: nuclear magnetic resonance, ion traps, and ultracold atoms in optical lattices.
We show that, in the gapless Kondo regime, a single local quench at one end of a Kondo spin chain induces a fast and long-lived oscillatory dynamics. This quickly establishes a high-quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g., in the gapped dimer regime, only finite-size end to end effects can create some entanglement on a much longer time scale for rather short chains. By decoupling one end of the chain during the dynamics, one can distinguish between this end-end effect which vanishes, and the global Kondo cloud mediated entanglement, which persists. This quench approach paves the way to detect the elusive Kondo cloud through the entanglement between two individual spins. Our results show that nonperturbative cooperative phenomena from condensed matter may be exploited for quantum information.
We calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbor coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of four spins.
We present a protocol for quantum state transfer and remote state preparation across spin chains which operate in their antiferromagnetic mode. The proposed mechanism harnesses the inherent entanglement of the ground state of the strongly correlated many-body systems which naturally exists for free. The uniform Hamiltonian of the system does not need any engineering and, during the whole process, remains intact while a single-qubit measurement followed by a single-qubit rotation are employed for both encoding and inducing dynamics in the system. This, in fact, has been inspired by recent progress in observing spin waves in optical lattice experiments, in which manipulation of the Hamiltonian is hard and instead local rotations and measurements have become viable. The attainable average fidelity stays above the classical threshold for chains up to length 50 and the system shows very good robustness against various sources of imperfection.
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.