[Paper Review] Quantum Mechanics as Quantum Information (and only a little more)

Christopher A. Fuchs|ArXiv.org|May 8, 2002

Quantum Mechanics and Applications115 references356 citations

TL;DR

This paper reframes quantum mechanics as a theory of quantum information, proposing that its core principles can be distilled into a few physically meaningful, information-theoretic statements. By treating quantum states as subjective degrees of belief and emphasizing the role of information in measurement and probability, the author argues that quantum mechanics reduces to a framework of rational belief updating under uncertainty, with Hilbert space dimension as the only objective physical parameter.

ABSTRACT

In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the integer parameter D traditionally ascribed to a quantum system via its Hilbert-space dimension.

Motivation & Objective

• To resolve the persistent crisis in quantum foundations by reducing quantum theory to a minimal set of physically meaningful statements.
• To argue that quantum mechanics is fundamentally about information, with only the Hilbert space dimension being an objective physical parameter.
• To replace interpretational pluralism with a unified, information-theoretic foundation grounded in Bayesian probability and operational consistency.
• To show that the structure of quantum mechanics—especially entanglement and measurement—arises from principles of information processing and rational belief updating.
• To correct the misconception that quantum mechanics requires multiple competing interpretations by demonstrating its coherence through quantum information theory.

Proposed method

• Uses quantum Bayesianism (QBism) to interpret quantum states as personal degrees of belief rather than physical properties.
• Applies the framework of positive operator-valued measures (POVMs) to model measurements as information-gathering actions.
• Reconstructs the tensor product structure of composite systems from the structure of local observables and information-theoretic consistency.
• Employs Gleason’s theorem to justify the noncontextual assignment of probabilities to measurement outcomes.
• Introduces a hypothetical 'standard quantum measurement' at a metrology institute to formalize the operational meaning of quantum measurements.
• Uses Bayesian conditionalization as the core mechanism for updating beliefs upon measurement, avoiding the need for collapse postulates.

Experimental results

Research questions

• RQ1 Can quantum mechanics be reduced to a small number of physically meaningful, non-abstract statements?
• RQ2 What is the role of information and subjective probability in the foundations of quantum theory?
• RQ3 Why do we need multiple interpretations of quantum mechanics if the theory can be grounded in information processing?
• RQ4 How can the structure of quantum mechanics—especially entanglement and the tensor product—be derived from information-theoretic principles?
• RQ5 What aspects of quantum mechanics are objective versus subjective, and how can this distinction be rigorously drawn?

Key findings

• The only objective physical parameter in quantum mechanics is the Hilbert space dimension D, which is invariant and not dependent on an agent’s beliefs.
• The tensor product rule for composite systems is not fundamental but emerges from the structure of local observables and information-theoretic consistency.
• Entanglement and nonlocal correlations arise naturally from the rules of Bayesian updating and the structure of informationally complete POVMs.
• The standard quantum measurement can be conceptualized as a metrological standard, analogous to the kilogram, for information acquisition.
• The Hamiltonian and the choice of POVM for a measurement device are subjective, reflecting an agent’s beliefs rather than objective physical properties.
• The paper corrects a technical error in its earlier version, showing that the tensor product structure is secondary to the local observable structure, not a primary postulate.