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Laser Physics

Enhancement of parameter-estimation precision by weak measurement and quantum measurement reversal under various non-Markovian decoherence sources

Qiong Wang, Lan Xu, Zhi He

Published Aug 20, 2018• 8 citations
Publisher

Abstract

Abstract We investigate the effect of the weak measurement (WM) and quantum measurement reversal (QMR) on the improvement of the precision of parameter estimation for a qubit interacting with various non-Markovian decoherence sources: amplitude damping, dephasing damping and random unitary damping, respectively. We derive the exact expressions of the optimal quantum Fisher information, show explicitly that the WM and QMR operation indeed helps for enhancing the precision of parameter estimation from amplitude damping and phase damping, but not for random unitary damping. In particular, we found that the enhancement effect is independent of the specific form of the spectral density of the reservoir, which extends the applicable scope of the WM and QMR approach.

DOI
10.1088/1555-6611/aad845

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Abstract We investigate the effect of the weak measurement (WM) and quantum measurement reversal (QMR) on the improvement of the precision of parameter estimation for a qubit interacting with various non-Markovian decoherence sources: amplitude damping, dephasing damping and random unitary damping, respectively. We derive the exact expressions of the optimal quantum Fisher information, show explicitly that the WM and QMR operation indeed helps for enhancing the precision of parameter estimation from amplitude damping and phase damping, but not for random unitary damping. In particular, we found that the enhancement effect is independent of the specific form of the spectral density of the reservoir, which extends the applicable scope of the WM and QMR approach.
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Abstract The dynamic behavior of the relative entropy of coherence for a two-level system is systematically investigated in different regimes. We derive the exact expressions of relative entropy quantifying coherence for an exactly solving model consisting of single qubit interacting with independent structured reservoir, show explicitly that the weak measurement (WM) and quantum measurement reversal (QMR) operation indeed help for protecting the coherence. In addition, the freezing phenomenon of the coherence can be detected by using the optimal WM and QMR operation.
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We have investigated the dynamic features of the quantum-memory-assisted entropic uncertainty relation (QMA EUR) in the amplitude damping (AD) channel. The initial state of qubit system and quantum memory system shared between Alice and Bob is assumed as extended by Werner-like (EWL) state. To reduce the amount of entropic uncertainty of Pauli observables in this noisy channel, we presented a reduction scheme by means of weak measurements (WMs) and weak measurement reversals (WMRs) before and after the entangled system subjecting to the noisy channel. It is shown that the prior WM and poster WMR can effectively reduce quantity of entropic uncertainty, but the poster WM operation cannot played a positive role on reduction of quantity of entropic uncertainty. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.
Quantum parameter estimation is of fundamental importance in physics. Quantum resources, involving for instance entangled probes, offer a significant improvement in estimation precision over classical strategies for closed quantum systems. However, when noises such as decoherence are taken into account, the quantum gain may be jeopardized. In this paper, we show how the amplitude-damping decoherence degrades the estimation precision from the Heisenberg limit to the standard limit with the initial Greenberger-Horne-Zeilinger (GHZ) state being employed and demonstrate that the method of weak measurement and quantum measurement reversal can recover this estimation precision to the Heisenberg limit, even though at the price of a very low success probability.