[Paper Review] Towards a unification of physics and information theory

Igor Devetak, Anne Staples|ArXiv.org|Dec 26, 2001

Quantum Mechanics and Applications8 references3 citations

TL;DR

This paper proposes a unified framework for physics and information theory by reinterpreting Everett's many-worlds quantum mechanics with explicit inclusion of preparation and knowledge instances. It introduces directed entanglement as a unifying concept, showing that both classical and quantum communication are entanglement transfer, and provides a simple proof of the second law of thermodynamics via thermodynamic entropy as lack of entanglement between knowledge and physical systems.

ABSTRACT

A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett's many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of \emph{directed entanglement} is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed entanglement. Within the model, quantum thermodynamic entropy is also related to directed entanglement, and a simple proof of the second law of thermodynamics is given.

Motivation & Objective

• To address foundational shortcomings of the Copenhagen interpretation, particularly the ambiguous role of mixed states and the separation between classical and quantum communication.
• To unify quantum mechanics, thermodynamics, and information theory under a single formalism grounded in entanglement and conceptual experience.
• To provide a principled, information-theoretic foundation for quantum mechanics that treats knowledge and physical systems symmetrically.
• To offer a new derivation of the second law of thermodynamics based on entanglement dynamics and coarse-graining via renormalization group ideas.
• To establish a framework where quantum communication, classical communication, and thermodynamic entropy are all understood as manifestations of directed entanglement transfer.

Proposed method

• Reinterpret Everett's many-worlds theory by explicitly distinguishing physical systems (P) from instances of knowledge (K), where K tracks observers' conceptual experience.
• Model the universe as a pure state |Ψ⟩_U evolving unitarily via U, with subsystem states derived via partial trace: ρ_A = tr_U/A |Ψ⟩⟨Ψ|_U.
• Introduce 'directed entanglement' E(A→B) as the entanglement transferred from system A to knowledge instance B, enabling unified treatment of classical and quantum communication.
• Define quantum thermodynamic entropy S_T^>(Q|B) as the lack of entanglement between physical system Q and knowledge instance B, linking it to entropy increase.
• Use the property that entanglement transfer is additive (E(Q>Q<→BcB̃) = E(Q>→Bc) + E(Q<→B̃)) and unitary invariance to analyze entropy evolution.
• Apply Wilson's renormalization group idea by decomposing Q< into hierarchical scales (Q0, Q1, ...), where each scale randomizes the next, enabling continuous entropy increase.

Experimental results

Research questions

• RQ1 How can a unified description of quantum mechanics, thermodynamics, and information theory be constructed using a minimal set of physical principles?
• RQ2 Can classical and quantum communication over quantum channels both be understood as entanglement transfer, and if so, how is this formalized?
• RQ3 How does the second law of thermodynamics emerge from unitary evolution and entanglement dynamics in a closed quantum system?
• RQ4 What is the role of 'knowledge' instances in a physical theory, and how do they relate to measurement and information flow?
• RQ5 Can thermodynamic entropy be defined intrinsically via entanglement between physical systems and knowledge, rather than via coarse-graining?

Key findings

• The paper establishes that mixed density operators arise naturally from entanglement with other systems, resolving the ambiguity of the Copenhagen interpretation regarding the origin of mixed states.
• Classical and quantum communication are unified as forms of directed entanglement transfer, with the Holevo bound and quantum data processing inequality derivable solely from entanglement properties.
• A simple and intuitive proof of the second law of thermodynamics is provided, showing that thermodynamic entropy increases due to cascade-like entanglement across hierarchical scales of a system.
• Quantum thermodynamic entropy S_T^>(Q|B) is defined as the lack of entanglement between a physical system Q and a knowledge instance B, providing a direct operational link to information theory.
• The model shows that entropy increase continues not due to coarse-graining, but due to repeated entanglement with increasingly macroscopic, uniformly distributed degrees of freedom, as per the renormalization group cascade.
• The framework naturally accounts for correlated random variables in information theory by treating them as arising from entanglement between knowledge instances and physical systems, aligning with Wheeler’s 'It from Bit' and Wigner’s correlation-based view of physics.