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arXiv:1805.11795 · Journal of Physics A Mathematical and Theoretical

Interference of the signal from a local dynamical process with the quantum state propagation in spin chains

Saikat Sur, V Subrahmanyam

Published Oct 18, 2018• 2 citations
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Abstract

Abstract The effect of a local instantaneous quantum dynamical process (QDP), either unitary or non-unitary, on the quantum state transfer through a unitary Hamiltonian evolution is investigated for both integrable and non-integrable dynamics. There are interference effects of the quantum state propagation and the QDP signal propagation. The state transfer fidelity is small for further sites, from the site where the information is coded, indicating a finite speed for the propagation of the quantum correlation. There is a small change in the state transfer fidelity for the case of the non-unitary QDP intervening in the the background of unitary dynamics. In the case of the unitary QDP, the change is more pronounced, with a substantial increase in the fidelity for appropriate sites and times. For the non-integrable case, namely a kicked Harper model, the state transfer fidelity is quite large for further sites for short times, indicating that a finite speed for the propagation of the quantum correlation cannot be defined.

DOI
10.1088/1751-8121/aae952

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Abstract The effect of a local instantaneous quantum dynamical process (QDP), either unitary or non-unitary, on the quantum state transfer through a unitary Hamiltonian evolution is investigated for both integrable and non-integrable dynamics. There are interference effects of the quantum state propagation and the QDP signal propagation. The state transfer fidelity is small for further sites, from the site where the information is coded, indicating a finite speed for the propagation of the quantum correlation. There is a small change in the state transfer fidelity for the case of the non-unitary QDP intervening in the the background of unitary dynamics. In the case of the unitary QDP, the change is more pronounced, with a substantial increase in the fidelity for appropriate sites and times. For the non-integrable case, namely a kicked Harper model, the state transfer fidelity is quite large for further sites for short times, indicating that a finite speed for the propagation of the quantum correlation cannot be defined.
The effect of a local instantaneous quantum dynamical process (QDP), either unitary or non- unitary, on the quantum state transfer through a unitary Hamiltonian evolution is investigated for both integrable and non-integrable dynamics. There are interference effects of the quantum state propagation and the QDP signal propagation. The state transfer fidelity is small for further sites, from the site where the information is coded, indicating a finite speed for the propagation of the quantum correlation. There is a small change in the state transfer fidelity for the case of non- unitary QDP intervening the background unitary dynamics. In the case of unitary QDP, the change is more pronounced, with a substantial increase in the fidelity for appropriate sites and times. The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo falls off as a function of the time of QDP occurrence, and saturates to a value, depending on the parameter values. For the non-integrable case, viz. a kicked Harper model, it exhibits an oscillatory behaviour around a larger value. The state transfer fidelity, in this case, is quite large for further sites for short times, indicating a finite speed for the propagation of the quantum correlation cannot be defined.
Abstract We consider a local instantaneous quantum dynamical process (QDP) that disturbs the background unitary Hamiltonian dynamics of a spin chain. We consider both a non-unitary incoherent QDP and a coherent unitary QDP intervention of the dynamical evolution of the spin chain. To track the effect of QDP on the dynamics, we investigate the Loschmidt echo, which is quite sensitive to whether the background dynamics is integrable or not. For the integrable case, namely the Heisenberg model, the Loschmidt echo depends on the parameters corresponding to the QDP as well as the time of occurrence of QDP. The probability of reviving the system to its initial state is higher for non-unitary/incoherent QDPs occurring at large time intervals. In the case of a unitary/coherent QDP, some amount of the probability of reviving the state is lost. For the non-integrable background dynamics we consider a kicked Harper model. It exhibits a decaying behaviour when contrasted with integrable dynamics. The decay rate is slower when the corresponding classical Hamiltonian is non-chaotic.
Abstract We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. quantum measurement operation) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the quantum operation. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. using the Ising, Heisenberg and transverse- XY dynamics.
We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain. The aim is to detect if the process occurred or not from a measurement on a far away spin at a later time. From the dynamical evolution of the state from the epoch time it is possible to detect the occurrence of the dynamical process. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. the Ising, Heisenberg, and the transverse-XY dynamics.
We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster the decay of correlations. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a timescale ∝ 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a timescale ∝ 1/δ 2 , where δ is the strength of perturbation. A detailed discussion of a semiclassical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behaviour is recovered in the classical limit → 0, as the two limits δ → 0 and → 0 do not commute. In addition, we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on the celebrated example of a quantized kicked top.