Quantum perfect correlations

Abstract

The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity of perfect correlations is proved to generally hold, and applied to a simple articulation for the failure of Hardy's nonlocality proof for maximally entangled states. The notion of perfect correlations between observables and POVMs is used for defining the notion of a precise measurement of a given observable in a given state. A longstanding misconception on the correlation made by the measuring interaction is resolved in the light of the new theory of quantum perfect correlations.

Latex, 31 pages. Typos are corrected in ver 2

References in corpus (2)

• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Noise and disturbance in quantum mechanics

Cited by in corpus (19)

• Soundness and completeness of quantum root-mean-square errors
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory
• Quantum Reality and Measurement: A Quantum Logical Approach
• Quantum-like model for unconscious-conscious interaction and emotional coloring of perceptions and other conscious experiences
• Entanglement of observables: Quantum conditional probability approach
• A complete and operational resource theory of measurement sharpness
• Heisenberg's uncertainty relation: Violation and reformulation
• Orthomodular-Valued Models for Quantum Set Theory
• Operational Meanings of Orders of Observables Defined through Quantum Set Theories with Different Conditionals
• EPR states and Bell correlated states in algebraic quantum field theory
• Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory (Extended Abstract)
• Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory
• Error-Disturbance Relation in Stern-Gerlach Measurements
• Error-disturbance uncertainty relations in Faraday measurements
• An attempt to understand relational quantum mechanics
• A dynamical approach to compatible and incompatible questions
• Intersubjectivity and value reproducibility of outcomes of quantum measurements
• Fundamental limits to contrast reversal of survival probability correlations