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Chinese Physics B

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

Zhi He, Chunmei Yao

Published Nov 1, 2014• 17 citations
Publisher

Abstract

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement (WM) and quantum measurement reversal (QMR). We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.

DOI
10.1088/1674-1056/23/11/110601

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The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement (WM) and quantum measurement reversal (QMR). We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.
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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.
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.
Abstract We investigate precision of phase estimation without and with decoherence using a non-Hermitian operation, i.e. parity-time ( ) symmetric operation. We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- symmetric operations, to show the performance of symmetric operation on QFI dynamics. By investigation, we find that pre- symmetric operator process could completely eliminate the effect of decoherence to improve the parameters estimation, while with the help of the post- symmetric operator process can potentially enhance and preserve the QFI by choosing appropriate non-Hermitian operator parameters.
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.
We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter [Formula: see text], we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal [Formula: see text] to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.