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arXiv:1506.06249

Heisenberg's Limit Phase Sensitivity in The Presence of Decoherence Channels

Farzam Nosraty

Published Jun 20, 2015• 0 citations
arXivHTMLPDF

Abstract

In the present study, time evolution of quantum Cramer-Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.

DOI
10.48550/arxiv.1506.06249

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In the present study, time evolution of quantum Cramer-Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.
Abstract In the present study, time evolution of quantum Cramer–Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.
Abstract Quantum theory sets a fundamental bound for the minimal time evolution between initial and final state of a system . This bound is called quantum speed limit time , which is used to quantify the speed of evolution of a quantum system. If quantum speed limit time decreases, the evolution keeps on increasing. In this paper, we study the effect of quantum speed limit time in terms of correlated and uncorrelated noise channels like amplitude damping and phase damping channel. We use maximally entangled mixed state as our initial state. We observe the behavior of quantum speed limit time under Markovian and non-Markovian dynamics. We prove that for the special class of our inital state and for the dynamical evolution of a system, there exist a link between quantum speed limit time and non-Markovianity. However, an interesting results were also observed regarding the tightness of bound in Markovian region. Our results shed light on the information back-flow between system and environment in terms of quantum evolution which is useful as a resource in quantum information processing task.
The quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information flows from the environments to qubits after a number of times if the bath parameter s is larger than a critical value which is related to temperature. The sudden-change behavior will happen during the evolution of the quantum Fisher information of the maximal entanglement state in the non-Markovian environments. The sudden-change times can be varied with the change of the bath parameter s . For a very large number of entangled qubits, the sudden-change behavior of the maximal quantum Fisher information can be used to characterize the existence of the entanglement. The metrology strategy based on the quantum correlated state leads to a lower phase uncertainty when compared with the uncorrelated product state.
We establish an information-theoretic approach for quantitatively characterizing the non-Markovianity of open quantum processes. Here, the quantum Fisher information (QFI) flow provides a measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly analytic solution shows that for each fixed time the QFI flow is decomposed into additive subflows according to different dissipative channels.
The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.