On the relation between measurement outcomes and physical properties

Abstract

One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable quantities, which cannot simply be identified with each other. Our analysis shows that the Hilbert space formalism itself describes a fundamental separation between quantitative properties and qualitative outcomes that needs to be taken into account in an objective description of quantum measurements. We derive fundamental relations between the statistics of measurement outcomes and the values of physical quantities that explain how the objective properties of a quantum system appear in the context of different measurement interactions. Our results indicate that non-classical correlations can be understood in terms of the actual role of physical properties as quantifiable causes of the external effects observed in a quantum measurement.

11 pages, updated references and clarification of weak value reference below Eq.(12)

References in corpus (10)

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Cited by in corpus (8)

• Understanding quantum mechanics: a review and synthesis in precise language
• Quantum interference of position and momentum: a particle propagation paradox
• Contextuality of quantum fluctuations characterized by conditional weak values of entangled states
• Control of particle propagation beyond the uncertainty limit by interference between position and momentum
• Uncertainty limits of the information exchange between a quantum system and an external meter
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Experimental evaluation of the non-classical relation between measurement errors using entangled photon pairs as a probe
• Experimental evidence for the physical delocalization of individual photons in an interferometer