Modular values and weak values of quantum observables

Abstract

The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an effective interaction when the coupling is weak, it describes a coupling of any strength but only to qubit meters. The generalization of the concept for a coupling of a composite system to a multi-qubit meter provides an explanation of some current experiments.

4 pages

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Cited by in corpus (46)

• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Nonperturbative theory of weak pre- and post-selected measurements
• Observing Dirac's classical phase space analog to the quantum state
• Quantum measurements with preselection and postselection
• Weak Measurements Beyond the Aharonov-Albert-Vaidman Formalism
• Using technical noise to increase the signal-to-noise ratio, via imaginary weak values
• State tomography via weak measurements
• Ultra-sensitive phase estimation with white light
• Direct measurement of a nonlocal entangled quantum state
• Contextual-value approach to the generalized measurement of observables
• Strengthening weak measurements of qubit out-of-time-order correlators
• Interferences in quantum eraser reveal geometric phases in modular and weak values
• Nonlocal Measurements via Quantum Erasure
• Experimental demonstration of separating the waveparticle duality of a single photon with the quantum Cheshire cat
• Observing trajectories with weak measurements in quantum systems in the semiclassical regime
• Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables
• Weak measurement with orthogonal pre-selection and post-selection
• Measurements of nonlocal variables and demonstration of the failure of the product rule for a pre- and postselected pair of photons
• A framework for measuring weak values without weak interactions and its diagrammatic representation
• Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
• Full characterization of modular values for two-dimensional systems
• Operational formulation of weak values without probe systems
• Progress and Perspectives on Weak-value Amplification
• Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor
• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• Effects of Postselected von Neumann Measurement on the Properties of Single-Mode Radiation Fields
• Efficient quantum computing with weak measurements
• A Scheme for Performing Strong and Weak Sequential Measurements of Non-commuting Observables
• Joint weak value for all order coupling using continuous variable and qubit probe
• Modular-value-based metrology with spin coherent pointers
• Experimenting quantum phenomena on NISQ computers using high level quantum programming
• Effects of postselected von Neumann measurement on nonclassicality of single-photon-added coherent state
• Obtaining imaginary weak values with a classical apparatus: applications for the time and frequency domains
• Generalized Modular Value with Nonclassical Pointer States
• Photonic realization of erasure-based nonlocal measurements
• The negative probabilities and information gain in weak measurements
• When a negative weak value -1 plays the counterpart of a probability 1
• Direct Measurement Methods of Density Matrix of an Entangled Quantum State
• Increase the Efficiency of Post-selection in Direct Measurement of Quantum Wave Function
• Overcoming experimental limitations in a non-linear two-qubit gate through postselection
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection
• Multiparameter quantum metrology with postselection measurements
• A note concerning the modular valued von Neumann interaction operator
• Quantum state tomography on closed timelike curves using weak measurements
• Nonlocal Generalized Quantum Measurements of Spin Products Without Maximal Entanglement