Weak measurement with orthogonal pre-selection and post-selection

Abstract

Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and post-selections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and post-selections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and post-selections tend to be orthogonal.

References in corpus (19)

• 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
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Precision frequency measurements with interferometric weak values
• Quantum Averages of Weak Values
• Quantum measurements with preselection and postselection
• Modular values and weak values of quantum observables
• Optimal Probe Wavefunction of Weak-Value Amplification
• Weak values of electron spin in a double quantum dot
• Weak measurement: Effect of the detector dynamics
• Full counting statistics of weak measurement
• Geometric phase in weak measurements
• Tomography of many-body weak values: Mach-Zehnder interferometry
• Geometrical aspects of weak measurements and quantum erasers
• Weak and semiweak values in non-ideal spin measurements: an exact treatment beyond the asymptotic regime
• Weak values and the quantum phase space
• Weak Values and Continuous-Variable Entanglement Concentration
• Weak Measurements with Entangled Probes

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• Coupling-Deformed Pointer Observables and Weak Values
• Amplification effects in optomechanics via weak measurement
• Complementary weak-value amplification with concatenated postselections
• Progress and Perspectives on Weak-value Amplification
• Weak Measurement and Two-State-Vector Formalism: Deficit of Momentum Transfer in Scattering Processes
• Amplification limit of weak measurements: a variational approach
• The negative probabilities and information gain in weak measurements
• Reply to a Commentary "Asking photons where they have been without telling them what to say"
• Quantum state tomography on closed timelike curves using weak measurements