Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations

Abstract

The simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics -- taking into account the free Hamiltonian -- on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.

arXiv comment24 pages, 3 figures, sent for publication

References in corpus (39)

• Quantum entanglement
• Gaussian Quantum Information
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Continuous variable quantum information: Gaussian states and beyond
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Separability Properties of Three-mode Gaussian States
• Gaussian states in continuous variable quantum information
• Dynamics of simultaneously measured non-commuting observables
• Past quantum states
• Joint quantum measurements with minimum uncertainty
• Uncertainty Relations for Joint Measurements of Noncommuting Observables
• Experimental test of universal complementarity relations
• The modern tools of quantum mechanics (A tutorial on quantum states, measurements, and operations)
• Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
• On the Theory of Wave Packets
• Realization of Measurement and the Standard Quantum Limit
• Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
• Joint measurements via quantum cloning
• Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables
• Retrodiction beyond the Heisenberg uncertainty relation
• Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
• A quantum measurement of the spin direction
• Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements
• Simultaneous weak measurement of non-commuting observables
• Factorizing the time evolution operator
• Local measurement uncertainties impose a limit on non-local quantum correlations
• The role of system-meter entanglement in controlling the resolution and decoherence of quantum measurements
• Focusing in Arthurs-Kelly-type Joint Measurements with Correlated Probes
• Remote Tomography Via von Neumann-Arthurs-Kelly Interaction
• How well can we guess the outcome of measurements of non-commuting observables?
• The Concept of Experimental Accuracy and Simultaneous Measurements of Position and Momentum
• Heisenberg's error-disturbance relations: a joint measurement-based experimental test
• Quantum dynamics under simultaneous and continuous measurement of noncommutative observables
• Macroscopic Quantum Measurements of noncommuting observables
• Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs
• Experimental evaluation of the non-classical relation between measurement errors using entangled photon pairs as a probe
• Pointer-based simultaneous measurements of conjugate observables in a thermal environment
• Maximal Entanglement and Teleportation using an Arthurs-Kelly type Interaction for Qubits
• Optimal Joint Measurements of Position and Momentum