Physical content of Heisenberg's uncertainty relation: Limitation and reformulation

Abstract

Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of Heisenberg's relation proven valid for arbitrary measurements is proposed and reveals two distinct types of possible violations of Heisenberg's relation.

7 pages, REVTEX. Revised with adding discussions. Title and Abstract are changed

References in corpus (1)

• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

Cited by in corpus (50)

• Soundness and completeness of quantum root-mean-square errors
• Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Quantum root-mean-square error and measurement uncertainty relations
• How well can one jointly measure two incompatible observables on a given quantum state?
• Joint quantum measurements with minimum uncertainty
• Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement
• Uncertainty Relations for Joint Measurements of Noncommuting Observables
• Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements
• Measurement uncertainty relations
• Quantum Theory and Determinism
• Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements
• Universal Uncertainty Principle in the Measurement Operator Formalism
• Tests of Fundamental Quantum Mechanics and Dark Interactions with Low Energy Neutrons -- Extended Version
• Measurement theory in local quantum physics
• Quantum Reality and Measurement: A Quantum Logical Approach
• A universally valid Heisenberg uncertainty relation
• The Compton-Schwarzschild correspondence from extended de Broglie relations
• Uncertainty from Heisenberg to Today
• Measurement uncertainty relations for discrete observables: Relative entropy formulation
• Uncertainty and Trade-offs in Quantum Multiparameter Estimation
• Conservation-Law-Induced Quantum Limits for Physical Realizations of the Quantum NOT Gate
• Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements
• Does Compton/Schwarzschild duality in higher dimensions exclude TeV quantum gravity?
• Measurement uncertainty relations for position and momentum: Relative entropy formulation
• The Compton-Schwarzschild relations in higher dimensions
• Heisenberg's uncertainty relation: Violation and reformulation
• Quantum Errors and Disturbances: Response to Busch, Lahti and Werner
• Experimental test of error-tradeoff uncertainty relation using a continuous-variable entangled state
• Direct experimental test of commutation relation via weak value
• Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)
• Experimental Test of Tight State-Independent Preparation Uncertainty Relations for Qubits
• Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation
• Using Neutrinos to test the Time-Energy Uncertainty Relation in an Extreme Regime
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Measurement Uncertainty: Reply to Critics
• Uncertainty principle, Shannon-Nyquist sampling and beyond
• Error-Disturbance Relation in Stern-Gerlach Measurements
• Position-Momentum Uncertainty Relation for an Open Macroscopic Quantum System
• Complementarity and the nature of uncertainty relations in Einstein-Bohr recoiling slit experiment
• Uncertainty relations: curiosities and inconsistencies
• Classical Information-Theoretical View of Physical Measurements and Generalized Uncertainty Relations
• Tight qubit uncertainty relations studied through weak values in neutron interferometry
• Linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state
• Proof of the Standard Quantum Limit for Monitoring Free-Mass Position
• Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
• Linear position measurements with minimum error-disturbance in each minimum uncertainty state
• Uncertainty-disturbance relations and applications
• The Optimal Pure Gaussian State Associated with Joint Position-Momentum Measurements
• Simultaneous measurability of error and disturbance