Classical Field Approach to Quantum Weak Measurements

Abstract

By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and post-selection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and post-selected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.

6 pages, 2 figures, published version

References in corpus (22)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Proof of Heisenberg's error-disturbance relation
• Direct Measurement of a 27-Dimensional Orbital-Angular-Momentum State Vector
• Weak Measurements of Light Chirality with a Plasmonic Slit
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Weak value amplification is suboptimal for estimation and detection
• Precision frequency measurements with interferometric weak values
• Photon wave functions, wave-packet quantization of light, and coherence theory
• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
• Weak Values Technique for Velocity Measurements
• A double-slit `which-way' experiment on the complementarity--uncertainty debate
• Measuring ultrasmall time delays of light by joint weak measurements
• Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement
• Observing Dirac's classical phase space analog to the quantum state
• Photon trajectories, anomalous velocities, and weak measurements: A classical interpretation
• Measuring measurement--disturbance relationships with weak values
• Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
• Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
• Picoradian deflection measurement with an interferometric quasi-autocollimator using weak value amplification
• Weak values are universal in von Neumann measurements
• The Photon Wavefunction: a covariant formulation and equivalence with QED

Cited by in corpus (17)

• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Anomalous Weak Values Are Proofs of Contextuality
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Weak Values are Interference Phenomena
• Weak value beyond conditional expectation value of the pointer readings
• Spacetime algebra as a powerful tool for electromagnetism
• Determination of weak values of quantum operators using only strong measurements
• A New Class of Retrocausal Models
• Experimental demonstration of separating the waveparticle duality of a single photon with the quantum Cheshire cat
• Disturbance in weak measurements and the difference between quantum and classical weak values
• Interferometric weak value of polarization observable and differential Jones matrix algebra
• Quantum causality relations and the emergence of reality from coherent superpositions
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• An exploration of the limits of control using quantum superpositions
• Weak-valued correlation functions: Insights and precise readout strategies
• Exploring Weak measurements within the Einstein-Dirac Cosmological framework
• Wick rotation derivation for weak values of the density and time-dependent density functional theory