Robert Spekkens: The invasion of physics by information theory

The speaker introduces the concept of resource theory and its relevance to information theory in physics. They highlight the differences between two types of revolutions in physics: one where a new theory supplants an old one through empirical predictions and tests, and another where a change in perspective occurs without overthrowing existing theories. The talk aims to show how information theory can provide a new framework for understanding physical theories and solving problems.

The speaker discusses the idea of resource theory in quantum information, using entanglement as an example. Initially, entanglement wasn't considered a resource, but it was later recognized for its utility in performing quantum operations. The concept of free operations (those that don't consume resources) and resource conversion is explained, with examples like symmetric operations and thermal operations in different contexts.

The focus shifts to how resources can be converted within a process theory framework. The speaker explains the concept of free processes and how they can be characterized to determine if one resource can be converted into another. They introduce the idea of partial orders and measures of resources, highlighting that no single measure can capture the entire partial order, thus requiring multiple measures for a complete understanding.

This section briefly touches on the resource theory of information, specifically in the context of quantum encodings of classical data. The speaker discusses how different quantum states can encode classical information and how the quality of these encodings can be compared using measures that respect data processing inequalities. The concept of non-increasing measures under data processing is emphasized.

The speaker introduces the resource theory of symmetry, using Curie's principle as a foundation. They describe symmetric operations in quantum theory and how these operations can be used to understand state conversions. The talk explains the limitations of Noether's theorem in the context of open systems and how measures of asymmetry can address these limitations, providing a broader framework for understanding symmetry in physical systems.

Examples of symmetric operations and state conversions are given, focusing on rotational symmetry. The speaker explains how symmetric operations can be realized through specific interactions and how they relate to Noether's theorem. The discussion extends to open systems and the need for measures of asymmetry that apply to both closed and open systems, illustrating the non-trivial nature of finding these measures.

The speaker continues discussing the deficiencies of Noether's theorem in open systems and introduces measures of asymmetry that apply to open system dynamics. They explain how these measures provide monotonicity constraints similar to the second law of thermodynamics and how they can be used to derive conservation laws for closed system dynamics.

A key part of the talk, this section bridges information theory and the resource theory of asymmetry. The speaker explains how questions about state transformations in the context of asymmetry can be rephrased as information theory problems. They provide a 'physicist's proof' to show the equivalence of these two perspectives, emphasizing the role of information theory in understanding asymmetry.

The speaker elaborates on how measures of asymmetry can be derived from standard measures of information. They provide examples of different measures, such as the Holevo quantity and the 1-norm distance, and discuss how these measures apply to various problems in symmetry breaking and quantum information theory. The talk highlights the importance of having multiple measures to fully understand asymmetry properties.

Moving on to the resource theory of athermality, the speaker introduces the second law of thermodynamics and its standard formulations. They point out the deficiencies of these formulations and propose a resource theory approach to overcome them. This approach defines free operations in terms of energy-conserving unitaries and thermal states, allowing for a more comprehensive understanding of state transitions and the role of thermal equilibrium.

The speaker explains how the resource theory of athermality provides necessary conditions for state transitions by introducing measures of athermality. These measures are functions that are non-increasing under thermal operations, similar to measures in information theory. The talk discusses how these measures apply to time translation invariant states and proposes a conjecture for their applicability to more general states.

This section covers the practical applications of the resource theory of athermality and symmetry. The speaker provides examples of how these theories can be used to solve problems in thermodynamics and quantum information. They also highlight open problems, such as finding complete sets of conditions for state convertibility and fully characterizing the partial orders of resources.

The speaker draws connections between different resource theories, showing how the principles of information theory apply across various domains. They discuss the implications of these connections for understanding state transitions, the role of symmetries, and the limits of physical processes. The talk emphasizes the overarching principle that information cannot be increased under data processing, tying together the themes of the conference.

The final section revisits classical thermodynamics from the perspective of resource theories. The speaker argues that many traditional thermodynamic principles can be reinterpreted using the language of resource theories and information theory. They discuss how this new perspective can provide deeper insights into the nature of physical laws and the limitations of current theories.