[Paper Review] The union of physics and information

Igor Devetak, Anne Staples|arXiv (Cornell University)|Jan 1, 2002

Quantum Mechanics and Applications3 references1 citations

TL;DR

This paper unifies quantum mechanics, thermodynamics, and information theory by reinterpreting Everett’s many-worlds theory with ensemble preparation, introducing directed entanglement to unify classical and quantum communication as entanglement transfer. It resolves the paradox of constant thermodynamic entropy in closed quantum systems by framing physical experience as correlations between knowledge states, linking quantum foundations to Shannon information theory through correlated random variables.

ABSTRACT

A union of 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 directed entanglement is introduced through which both classical and quantum communication over quantum channels are reduced to entanglement transfer. The paradox of constant thermodynamic entropy in a closed quantum system is resolved. The view taken in this Letter is that the totality of conceptual experience can be described in terms of correlated random variables. This will allow us to make contact with Shannon’s information theory [1] in which random variables are the carriers of information. Two protagonists sharing the same physical world is no more than classical correlations between the states of their knowledge regarding that world. Similarly, the observation of definite physical laws is no more than classical correlations between states of knowledge regarding two consecutive acts of measurement, or preparation and measurement, depending on the experiment. For instance, a ball kicked by Alice seen as obeying Newton’s deterministic laws of motion is merely a statement about the correlation

Motivation & Objective

• To reconcile quantum mechanics, thermodynamics, and information theory by reinterpreting Everett’s many-worlds theory with ensemble preparation.
• To resolve the paradox of constant thermodynamic entropy in closed quantum systems by modeling physical experience as correlations between knowledge states.
• To establish a unified framework where classical and quantum communication are reduced to entanglement transfer via directed entanglement.
• To connect quantum foundations with Shannon information theory by treating physical laws and observations as classical correlations between knowledge states.
• To provide a conceptual framework in which the totality of physical experience is described through correlated random variables.

Proposed method

• Reinterpreting Everett’s many-worlds theory by incorporating preparation according to a given ensemble, extending its formalism to include statistical ensembles.
• Introducing the concept of directed entanglement to model the flow of information in quantum channels, enabling unified treatment of classical and quantum communication.
• Modeling physical observations as classical correlations between states of knowledge regarding preparation and measurement outcomes.
• Formalizing the totality of conceptual experience as correlated random variables, enabling application of Shannon’s information theory to physical systems.
• Analyzing the thermodynamic behavior of closed quantum systems by examining correlations in knowledge states, leading to resolution of the entropy constancy paradox.
• Using the framework of correlated knowledge to reinterpret deterministic laws (e.g., Newton’s laws) as statements about correlation between measurement outcomes.

Experimental results

Research questions

• RQ1 How can quantum mechanics, thermodynamics, and information theory be formally unified within a single conceptual framework?
• RQ2 What is the role of ensemble preparation in extending Everett’s many-worlds interpretation to include statistical and information-theoretic structures?
• RQ3 How does directed entanglement enable a unified description of classical and quantum communication over quantum channels?
• RQ4 Why does thermodynamic entropy appear constant in closed quantum systems, and how can this be resolved within a knowledge-based framework?
• RQ5 In what way can physical laws and observations be understood as classical correlations between states of knowledge regarding measurement and preparation?

Key findings

• The paradox of constant thermodynamic entropy in closed quantum systems is resolved by modeling entropy not as an intrinsic property of the system, but as a correlation measure between knowledge states.
• Classical and quantum communication are unified under the concept of directed entanglement, which reduces both to entanglement transfer across quantum channels.
• Observations of deterministic physical laws, such as Newton’s laws, are interpreted as classical correlations between knowledge states regarding consecutive measurements or preparation and measurement events.
• The framework establishes that the totality of physical experience can be described using correlated random variables, enabling direct application of Shannon’s information theory to quantum foundations.
• The reinterpretation of Everett’s theory with ensemble preparation provides a foundation for connecting quantum mechanics with information-theoretic concepts like entropy and correlation.
• Directed entanglement emerges as a key mechanism for modeling information flow, allowing a unified description of information transfer in quantum systems.