The Operational Choi-Jamiołkowski Isomorphism

Area of Science:

• Quantum mechanics
• Foundations of physics
• Generalized probabilistic theories

Background:

• The traditional formulation of quantum mechanics posits quantum states as fundamental objects.
• Generalized probabilistic theories offer alternative frameworks for studying physical theories.
• The Choi-Jamiołkowski isomorphism connects quantum states with quantum channels.

Purpose of the Study:

• To explore an operational approach to quantum mechanics where quantum states are not fundamental.
• To investigate the intratheoretic causal structure of quantum mechanics independently of ontological assumptions.
• To demonstrate that core features of quantum states can be derived from operational principles.

Main Methods:

• Utilizing an operational formulation of the Choi-Jamiołkowski isomorphism.
• Situating the research within the framework of generalized probabilistic theories.
• Analyzing constraints on non-local correlations within operational theories.

Main Results:

• Several properties usually attributed to quantum states can be derived from constraints on non-local correlations.
• The Choi-Jamiołkowski isomorphism is shown to be key in deriving these properties operationally.
• The findings suggest an equivalence between multipartite and temporal correlations.

Conclusions:

• Quantum states are not necessarily fundamental entities in quantum mechanics.
• The operational framework allows deriving quantum state properties from non-local correlations.
• This approach offers an ontology-independent understanding of quantum mechanics' causal structure.