Agents, Subsystems, and the Conservation of Information

Area of Science:

• Theoretical Physics
• Foundations of Physics
• Quantum Information Theory

Background:

• Defining subsystems is crucial in the scientific method but lacks a priori definition.
• Current subsystem definitions are often dictated by experimental capabilities, varying between agents.
• Existing frameworks struggle to unify classical and quantum mechanical subsystems.

Purpose of the Study:

• To propose a general method for defining subsystems in physical theories beyond quantum and classical mechanics.
• To associate agents with specific subsystems, including their states and transformations.
• To extend the purification principle to a broader theoretical context.

Main Methods:

• Developed a general construction associating agents with subsystems (states and transformations).
• Applied the construction to quantum mechanics (tensor product factors, operator subalgebras).
• Interpreted classical systems as quantum subsystems using specific operational access (covariant channels, free operations).

Main Results:

• The construction unifies subsystem notions in quantum mechanics.
• Classical systems are shown to be interpretable as quantum subsystems.
• For closed systems, all subsystem states admit a canonical purification.

Conclusions:

• The proposed method provides a unified framework for defining subsystems across diverse physical theories.
• Canonical purification is shown to be a general principle applicable beyond standard quantum mechanics.
• Coherent superpositions can be viewed as purifications of incoherent mixtures in this generalized setting.