Unsharp Quantum Reality

Abstract

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency - or potentiality - of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

Sections 2 and 4 of this Version 2 have been revised to increase clarity and reduce ambiguity. The terminology of unsharp properties, vagueness and fuzziness has been explained more explicitly. Main message has remained unchanged

References in corpus (6)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Contextuality for preparations, transformations, and unsharp measurements
• Heisenberg's Uncertainty Principle
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• How Stands Collapse II
• The Structure of Classical Extensions of Quantum Probability Theory

Cited by in corpus (20)

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• Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
• Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements
• Optimal violation of Leggett-Garg inequality for arbitrary spin and emergence of classicality through unsharp measurement
• Quantum measurements constrained by the third law of thermodynamics
• A relational perspective on the Wigner-Araki-Yanase theorem
• Quantum Reality, Perspectivalism and Covariance
• Testing local-realism and macro-realism under generalized dichotomic measurements
• Fuzzy measurements and coarse graining in quantum many-body systems
• Geometry of joint reality: device-independent steering and operational completeness
• Quantum incompatibility from the viewpoint of entanglement theory
• Quantum Logic and Quantum Reconstruction
• The Leggett-Garg inequality and Page-Wootters mechanism
• Unified treatment of the total angular momentum of single photons via generalized quantum observables
• Quantum violation of macrorealism under multi-outcome two-parameter generalised measurements
• Projective measurements under qubit quantum channels
• Can we accurately read or write quantum data?
• Falsifiability of Isolated Spacetime Regions