Quantum measurements with preselection and postselection

Abstract

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-tonoise 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.

9 pages, 4 figures

References in corpus (9)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Precision frequency measurements with interferometric weak values
• Modular values and weak values of quantum observables
• Weak measurement: Effect of the detector dynamics
• Tomography of many-body weak values: Mach-Zehnder interferometry

Cited by in corpus (61)

• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Weak value amplification is suboptimal for estimation and detection
• Precision metrology using weak measurements
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• The significance of the imaginary part of the weak value
• Measuring ultrasmall time delays of light by joint weak measurements
• Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation
• Improving the precision of weak measurements by postselection measurement
• Experimentally quantifying the advantages of weak-value-based metrology
• Entanglement-assisted weak value amplification
• New wine in old bottles: Quantum measurement - direct, indirect, weak - with some applications
• State tomography via weak measurements
• Optimal Probe Wavefunction of Weak-Value Amplification
• Weak measurements with orbital angular momentum pointer states
• Quantum sensors based on weak-value amplification cannot overcome decoherence
• Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect
• Weak value amplification in a shot-noise limited interferometer
• Protecting weak measurements against systematic errors
• State estimation: direct state measurement vs. tomography
• Achieving Heisenberg-scaling precision with projective measurement on single photons
• Post-selected von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states
• Weak and semiweak values in non-ideal spin measurements: an exact treatment beyond the asymptotic regime
• Weak-value-amplification analysis beyond the AAV limit of weak measurements
• SVD Entanglement Entropy
• Advantages of nonclassical pointer states in postselected weak measurements
• Weak measurement with orthogonal pre-selection and post-selection
• Suppressing technical noises in weak measurement by entanglement
• Coupling-Deformed Pointer Observables and Weak Values
• Scheme and Experimental Demonstration of Fully Atomic Weak Value Amplification
• Theory of "Weak Value" and Quantum Mechanical Measurements
• A framework for measuring weak values without weak interactions and its diagrammatic representation
• Direct state reconstruction with coupling-deformed pointer observables
• Path probabilities for consecutive measurements, and certain "quantum paradoxes"
• Theory of Compression Channels for Postselected Quantum Metrology
• Progress and Perspectives on Weak-value Amplification
• Amplification limit of weak measurements: a variational approach
• Weak Measurement and Two-State-Vector Formalism: Deficit of Momentum Transfer in Scattering Processes
• Application of the weak-measurement technique to study atom-vacuum interactions
• Weak values and weak coupling maximizing the output of weak measurements
• Influence of squeezing on the weak-to-strong measurement transition
• Statistical hypothesis testing by weak-value amplification: Proposal and evaluation
• Disembodiment of arbitrary number of properties in quantum Cheshire cat experiment
• Identifying weak values with intrinsic dynamical properties in Modal theories
• Weak value amplification and beyond the standard quantum limit in position measurements
• Joint weak value for all order coupling using continuous variable and qubit probe
• Single-photon-added coherent state based measurement transition and its advantages in precision measurement
• Null weak values in multi-level systems
• Cat state, sub-Planck structure and weak measurement
• Interpreting weak value amplification with a toy realist model
• Distribution of xp in some molecular rotational states
• The negative probabilities and information gain in weak measurements
• Generalized Modular Value with Nonclassical Pointer States
• Information gain versus coupling strength in quantum measurements
• Standard and Null Weak Values
• Theoretical investigation of the relations between quantum decoherence and weak-to-strong measurement transition
• Quality analysis for precision metrology based on joint weak measurements without discarding readout data
• Weak values obtained from mass-energy equivalence
• Pre- and post-selected measurements with coupling-strength-dependent modulation
• No-go result for quantum postselection measurements of rank-m degenerate subspace
• Amplification of mechanical quadratures using weak values
• State distinguishability under weak measurement and post-selection: A unified system and device perspective