Distinguishing Features and Axioms of Quantum Mechanics

K. Heyde, John L. Wood

Andrei Yu. Khrennikov

We start with discussion on Bohr’s response to the EPR argument andexplain how Bohr was able to sail between Scylla (incompleteness) andCharybdis (nonlocality) towards the consistent interpretation of quantumtheory. We call the latter the Bohr interpretation and distinguish it fromthe commonly used orthodox Copenhagen interpretation. We point to connectionbetween the complementarity principle and the information interpretationof QM and briefly discuss its versions, starting withSchrödinger and continuing to the information quantization interpretation(Zeilinger, Brukner), QBism (Fuchs et al.), reality without realism (RWR,Plotnitsky), the Växjö interpretation (Khrennikov), and derivations of thequantum formalism from the information axioms (e.g., D’Ariano et al.). Oneof the main distinguishing features of the information interpretation is the possibility of structuring thequantum foundations without nonlocality and spooky actionat a distance.

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Paul Cooney

Arc V — Gravity & Quantum Theory Paper 7 Title Purification as the Structural Seed of Quantum Theory:Minimal Axioms Beyond Finite Accessibility Zenodo DOI 10.5281/zenodo.18226009 Description This paper presents a full axiomatic reconstruction of quantum theory starting from finite accessibility augmented by a single additional structural principle: purification. Building on the identification of the quantum gap in Paper V.6, it demonstrates that purification is not merely sufficient but structurally generative—acting as the seed from which the full architecture of quantum mechanics emerges. The analysis shows that when purification is imposed on an accessibility-limited operational framework, core quantum features arise necessarily rather than by assumption. These include superposition, entanglement, reversible dynamics, and the tensor-product structure of composite systems. No geometric ontology, wavefunction realism, or microscopic state postulates are introduced. The paper carefully distinguishes purification from interpretational assumptions. It is treated not as a metaphysical claim about reality, but as a constraint on admissible descriptions: all apparent irreversibility must be explainable as loss of access to a larger, pure structure. From this requirement alone, the mathematical formalism of quantum mechanics is shown to follow. By identifying purification as the minimal axiom beyond finite accessibility, the paper sharply limits the space of possible quantum theories. Any alternative framework lacking purification is shown to fail to reproduce essential quantum phenomena, while any stronger assumption introduces surplus structure. Keywords quantum reconstruction; purification axiom; entanglement; superposition; operational quantum mechanics; axiomatic foundations Notes Arc V — Gravity & Quantum Theory (axiomatic quantum reconstruction) Purification elevated from repair mechanism to generative principle Quantum structure derived without geometry or microstates Strong separation between operational axioms and interpretation Direct precursor to non-geometric formulations of quantum mechanics

Paul Busch, PEKKA J. LAHTI, Peter Mittelstaedt

Adam M. Brandenburger, Pierfrancesco La Mura

The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such as superposition, entanglement, and nonlocality --- poses deep puzzles about the underlying physical reality, even while these same features are at the heart of exciting developments such as quantum cryptography, algorithms, and computing. These puzzles might be resolved if the mathematical structure of quantum mechanics were built up from physically interpretable axioms, but it is not. We propose three physically-based axioms which together characterize the simplest quantum system, namely the qubit. Our starting point is the class of all no-signaling theories. Each such theory can be regarded as a family of empirical models, and we proceed to associate entropies, i.e., measures of information, with these models. To do this, we move to phase space and impose the condition that entropies are real-valued. This requirement, which we call the Information Reality Principle, arises because in order to represent all no-signaling theories (including quantum mechanics itself) in phase space, it is necessary to allow negative probabilities (Wigner [1932]). Our second and third principles take two important features of quantum mechanics and turn them into deliberately chosen physical axioms. One axiom is an Uncertainty Principle, stated in terms of entropy. The other axiom is an Unbiasedness Principle, which requires that whenever there is complete certainty about the outcome of a measurement in one of three mutually orthogonal directions, there must be maximal uncertainty about the outcomes in each of the two other directions.