Macroscopicity and observational deficit in states, operations, and correlations

Area of Science:

• Quantum Information Theory
• Statistical Mechanics
• Foundations of Physics

Background:

• Macroscopic irreversibility emerges from microscopic reversible dynamics.
• Coarse-graining is crucial for understanding this emergence.
• Existing frameworks lack a unified approach to inferring macroscopic states from measurements.

Purpose of the Study:

• To develop a unified inferential framework for macroscopic states in quantum systems.
• To define macroscopic entropy based on an observer's informational perspective.
• To establish a resource theory of microscopicity.

Main Methods:

• Utilizing quantum statistical sufficiency and Bayesian retrodiction.
• Introducing the concept of 'observational deficit' to quantify irretrodictability.
• Formalizing macroscopic states within 'inferential reference frames'.

Main Results:

• A general definition of macroscopic entropy as an inferentially grounded measure of asymmetry.
• A resource theory of microscopicity unifying existing theories (coherence, athermality, asymmetry).
• Introduction of 'observational discord' to quantify quantum correlations under constraints.

Conclusions:

• The developed framework provides a unified approach to macroscopic states and entropy.
• The resource theory offers new insights into quantum correlations and information recoverability.
• This work deepens the understanding of irreversibility in quantum mechanics.