Ambiguity in quantum-theoretical descriptions of experiments

TL;DR

This paper explores the inherent ambiguity in quantum descriptions of experiments, highlighting multiple explanations and results, and discusses implications for concepts like invariance and quantum key distribution security.

Contribution

It explicitly analyzes the multiplicity of descriptions in quantum theory and their implications, clarifying the logical gap between experimental results and explanations.

Findings

Quantum descriptions involve multiple explanations for the same results.

Multiplicity of descriptions affects the concept of invariance in quantum mechanics.

Implications for quantum key distribution security are discussed.

Abstract

This paper contributes to a burgeoning area of investigation, the ambiguity inherent in mathematics and the implications for physics of this ambiguity. To display the mathematical form of equations of quantum theory used to describe experiments, we make explicit the knobs by which the devices of an experiment are arranged and adjusted. A quantum description comes in two parts: (1) a statement of results of an experiment, expressed by probabilities of detections as functions of knob settings, and (2) an explanation of how we think these results come about, expressed by linear operators, also as functions of knob settings. Because quantum mechanics separates the two parts of any description, it is known that between the statements of results and the explanations lurks a logical gap: given any statement of results one has a choice of explanations. Here we work out some consequences of this openness to choice. We show how quantum theory as mathematical language in which to describe experiments necessarily involves multiple descriptions: multiple explanations of a given result, as well as multiple statements of results and multiple arrangement of knobs. Appreciating these multiplicities resolves what otherwise is a confusion in the concept of invariance. Implications of multiplicity of description for the security of quantum key distribution are noted.