Operations, Disturbance, and Simultaneous Measurability

Abstract

Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to provide foundations of joint statistics of local general measurements on entangled systems in a general theoretical framework, the question is answered as to under what condition the outputs of two measuring apparatuses satisfy the joint probability formula for simultaneous measurements of their observables. For this purpose, all the possible state changes caused by measurements of an observable are characterized and the notion of disturbance in measurement is formalized in terms of operations derived by the measuring interaction.

32 pages, REVTeX

References in corpus (5)

• Experimental quantum teleportation
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• An Operational Approach to Quantum State Reduction
• Measurements of Nondegenerate Discrete Observables
• Controlling Quantum State Reduction

Cited by in corpus (22)

• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Conservation laws, uncertainty relations, and quantum limits of measurements
• Quantum perfect correlations
• Position measuring interactions and the Heisenberg uncertainty principle
• Perfect correlations between noncommuting observables
• Strongly Incompatible Quantum Devices
• Optimized entropic uncertainty relation for successive measurement
• Qualitative Noise-Disturbance Relation for Quantum Measurements
• Subspace preserving completely positive maps
• Subspace local quantum channels
• Gluing of completely positive maps
• Quantum measurements constrained by the third law of thermodynamics
• The role of quantum non-Gaussian distance in entropic uncertainty relation
• Controlling Quantum State Reduction
• Measurement disturbance and conservation laws in quantum mechanics
• Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem
• Quantum-like cognition and decision making in the light of quantum measurement theory
• Classicality of the heat produced by quantum measurements
• Parts and Composites of Quantum Systems
• Incorporating episodic memory into quantum models of judgment and decision
• Quantum Measurement Theory for Systems with Finite Dimensional State Spaces