Uncertainty of Weak Measurement and Merit of Amplification

Abstract

Aharonov's weak value, which is a physical quantity obtainable by weak measurement, admits amplification and hence is deemed to be useful for precision measurement. We examine the significance of the amplification based on the uncertainty of measurement, and show that the trade-offs among the three (systematic, statistical and nonlinear) components of the uncertainty inherent in the weak measurement will set an upper limit on the usable amplification. Apart from the Gaussian state models employed for demonstration, our argument is completely general; it is free from approximation and valid for arbitrary observables $A$ and couplings $g$.

Paper: 5 pages, 1 figure. Supplemental Material: 12 pages, 0 figure

References in corpus (12)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Complex weak values in quantum measurement
• Nonperturbative theory of weak pre- and post-selected measurements
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Weak value amplification is suboptimal for estimation and detection
• Measuring ultrasmall time delays of light by joint weak measurements
• Information amplification via postselection: A parameter estimation perspective
• All-order evaluation of weak measurements: --- The cases of an operator $\mathbf{A}$ which satisfies the property ${\mathbf{A}}^2=1$ ---
• Optimal Probe Wavefunction of Weak-Value Amplification
• Weak measurements with orbital angular momentum pointer states
• On Amplification by Weak Measurement
• Quantum sensors based on weak-value amplification cannot overcome decoherence

Cited by in corpus (16)

• Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
• Weak value controversy
• Weak value beyond conditional expectation value of the pointer readings
• Can Anomalous Amplification be Attained Without Postselection?
• Post-selected von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states
• Weak-value amplification: state of play
• On the novelty, efficacy, and significance of weak measurements for quantum tomography
• Statistical hypothesis testing by weak-value amplification: Proposal and evaluation
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• On the Validity of Weak Measurement Applied for Precision Measurement
• A Fundamental Upper Bound for Signal to Noise Ratio of Quantum Detectors
• Physical description of statistical hypothesis testing for a weak-value amplification experiment using a birefringent crystal
• Seeing opportunity in every difficulty: protecting information with weak value techniques
• The real and imaginary parts of a weak value appearing as back-actions via a post-selection
• Novel approach to neutron electric dipole moment search using weak measurement
• Amplification of gravitational motion via Quantum weak measurement