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arXiv:1505.01911

The amplification of weak measurements under quantum noise

Xuanmin Zhu, Yu-Xiang Zhang

Published May 8, 2015• 0 citations
arXivHTMLPDF

Abstract

The influence of outside quantum noises on the amplification of weak measurements is investigated. Three typical quantum noises are discussed. The maximum values of the pointer's shifts decrease sharply with the strength of the depolarizing channel and phase damping. In order to obtain significant amplified signals, the preselection quantum systems must be kept away from the two quantum noises. Interestingly, the amplification effect is immune to the amplitude damping noise.

DOI
10.48550/arxiv.1505.01911

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The influence of outside quantum noises on the amplification of weak measurements is investigated. Three typical quantum noises are discussed. The maximum values of the pointer's shifts decrease sharply with the strength of the depolarizing channel and phase damping. In order to obtain significant amplified signals, the preselection quantum systems must be kept away from the two quantum noises. Interestingly, the amplification effect is immune to the amplitude damping noise.
We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.
We study quantum measurements with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength. For a qubit system, we derive the maximum measurement results by choosing appropriate initial and finial states. Significant amplification effect is obtained when the interaction between the system and the measuring device is very weak; and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measure sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can both be significantly improved by weak measurements; surprisingly, neither SNR nor MS can be effectively improved when the probability decrease is considered.
Due to the interaction with the environment, a quantum state is often affected by the different types of noises which becomes to one of the biggest problems for practical quantum computation. We study the possibility of protecting the mixed state of a quantum system that goes through noise by weak measurements and control operations. The aim is to find the optimal measurement strength and control operations and make the input and output states as close as possible. We show that our scheme can effectively protect arbitrary mixed states against typical types of noise sources: amplitude damping, phase damping and amplitude-phase damping. The optimal measurement and control operators are deduced in different bases of the Bloch sphere to find the best control scheme for each type of noise. The effectiveness of our control scheme is demonstrated by simulation results.
Abstract We propose an efficient method to protect spin squeezing under the action of amplitude-damping, depolarizing and phase-damping channels based on measurement reversal from weak measurement, and consider an ensemble of N independent spin-1/2 particles with exchange symmetry. We show that spin squeezing can be enhanced greatly under three different decoherence channels and spin-squeezing sudden death can be avoided undergoing amplitude-damping and phase-damping channels. Moreover, we find that the spin-squeezing parameters can be completely recovered to its initial value under amplitude-damping channel by changing weak measurement strength irrespective of sufficiently strong decoherence. For the phase-damping channel, the spin-squeezing parameter can be recovered to a certain stationary value in certain conditions. Our results provide an active way to suppress decoherence and enhance the spin squeezing under decoherence, which is rather significant for quantum metrology in open systems.
We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measured displacement and the amplification factor are in fact not proportional to the weak value and rather vanish in the limit of infinitesimal output intensity. We derive the optimal overlap of the pre- and postselected states with which the amplification become maximum. We also show that the nonlinear effects begin to arise in the performed experiments so that any improvements in the experiment, typically with an amplification greater than 100, should require the nonlinear theory in translating the observed value to the original displacement.
Quantum communication provides a new way for transmitting highly sensitive information. But the existence of quantum noise inevitably affects the security and reliability of a quantum communication system. The technique of weak measurement and its reversal measurement (WMRM) has been proposed to suppress the effect of quantum noise, especially, the amplitude-damping noise. Taking a GHZ based remote state preparation (RSP) scheme as an example, we discuss the effect of WMRM for suppressing four types of quantum noise that usually encountered in real-world, i.e., not only the amplitude-damping noise, but also the bit-flip, phase-flip (phase-damping) and depolarizing noise. And we give a quantitative study on how much a quantum output state can be improved by WMRM in noisy environment. It is shown that the technique of WMRM has certain effect for improving the fidelity of the output state in the amplitude-damping noise, and only has little effect for suppressing the depolarizing noise, while has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise. Our result is helpful for improving the efficiency of entanglement-based quantum communication systems in real implementation.