[Paper Review] Parts and Wholes. An Inquiry into Quantum and Classical Correlations

M. P. Seevinck|ArXiv.org|Nov 6, 2008

Quantum Mechanics and Applications92 references16 citations

TL;DR

This paper introduces an epistemological criterion for holism in physical theories, distinguishing it from the supervenience-based approach. It demonstrates that quantum mechanics exhibits epistemological holism even without entanglement—using local operations and classical communication (LOCC)—revealing that holism arises from quantum property assignment rules, not just entanglement, challenging conventional views on quantum nonlocality and foundational structure.

ABSTRACT

** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. ** A large part of this dissertation is devoted to understanding different aspects of four different kinds of correlations: local, partially-local, no-signaling and quantum mechanical correlations. Novel characteristics of these correlations have been used to study how they are related and how they can be discerned via Bell-type inequalities that give non-trivial bounds on the strength of the correlations. ** The study of quantum correlations has also prompted us to study a) the multi-partite qubit state space with respect to its entanglement and separability characteristics, and b) the differing strength of the correlations in separable and entangled qubit states. Results include a novel classification of multipartite (partial) separability and entanglement, strong constraints on the monogamy of entanglement and of non-local correlations, and many new entanglement detection criteria that are directly experimentally accessible. ** Because of the generality of the investigation these results also have strong foundational as well as philosophical repercussions for the different sorts of physical theories as a whole; notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy.

Motivation & Objective

• To develop a new epistemological criterion for holism in physical theories that focuses on property determination under a specified resource basis.
• To distinguish epistemological holism from supervenience-based holism, showing they are logically independent.
• To investigate whether holism in quantum mechanics arises from entanglement or from the structure of property assignment rules.
• To demonstrate that epistemological holism can occur in the absence of entanglement, using LOCC on non-entangled product states.
• To challenge the assumption that entanglement is necessary for holism by constructing a counterexample using separable states.

Proposed method

• Formalizing holism via a resource basis that specifies what operations or resources are available for property determination.
• Applying the epistemological criterion to quantum mechanics using the standard Hilbert space formalism and the orthodox interpretation’s property assignment rule.
• Analyzing the distinguishability of quantum states under LOCC to assess epistemological holism.
• Contrasting the results with the supervenience criterion, which relies on entanglement as a necessary condition for holism.
• Using the Bell states and a set of nine non-entangled product states to compare LOCC distinguishability and reveal non-trivial epistemological holism.
• Formalizing the distinction between global and local property structures in theories with Cartesian product state spaces (e.g., classical physics, Bohmian mechanics) versus those with Hilbert space structures (e.g., quantum mechanics).

Experimental results

Research questions

• RQ1 Can epistemological holism occur in quantum mechanics without entanglement?
• RQ2 Is the supervenience criterion for holism logically independent from the epistemological criterion proposed in this paper?
• RQ3 What role does the property assignment rule play in determining whether a theory is holistic?
• RQ4 Are there non-entangled quantum states that exhibit epistemological holism under LOCC?
• RQ5 Can a physical theory be holistic in the epistemological sense but not in the supervenience sense?

Key findings

• Epistemological holism can occur without entanglement, as demonstrated by the inability to distinguish certain non-entangled product states using only LOCC.
• The set of nine non-entangled product states in a two-qubit system cannot be distinguished by LOCC, indicating epistemological holism despite the absence of entanglement.
• In contrast, the entangled Bell states can be distinguished using LOCC, showing that entanglement does not guarantee epistemological holism.
• The orthodox interpretation of quantum mechanics is holistic under both the epistemological and supervenience criteria, but for different reasons: entanglement in the supervenience approach, and property assignment rules in the epistemological one.
• The paper shows that the supervenience and epistemological criteria for holism are logically independent, as one can be satisfied while the other is not.
• The study reveals that the Hilbert space structure and its associated property assignment rules are central to epistemological holism, suggesting that superposition and non-classical property assignment may be more fundamental than entanglement for holism.