Cyclic quantum causal models.

Area of Science:

• Quantum Information Science
• Foundations of Physics
• Causality Theory

Background:

• Quantum theory challenges classical causal reasoning, particularly with Bell inequality violations.
• Existing quantum causal models explain quantum processes but require definite causal order (acyclic structures).
• Future theories merging quantum mechanics and gravity may involve causally nonseparable processes with indefinite causal order.

Purpose of the Study:

• To extend quantum causal models to cyclic causal structures.
• To provide a causal perspective on causally nonseparable processes.
• To investigate the relationship between causal nonseparability and cyclic causal structures.

Main Methods:

• Development of extended quantum causal models capable of handling cyclic causal structures.
• Analysis of bipartite processes within the extended causal framework.
• Investigation of unitary processes and their causal properties.

Main Results:

• The extended models provide a causal perspective on causally nonseparable processes.
• All unitarily extendible bipartite processes are shown to be causally separable.
• For unitary processes, causal nonseparability is equivalent to the cyclicity of their causal structure.

Conclusions:

• Quantum causal models can be extended to cyclic causal structures, addressing causally nonseparable processes.
• The framework offers new insights into the interplay between quantum correlations, causality, and spacetime structure.
• This work bridges the gap between quantum phenomena and causal explanations, paving the way for future research in quantum gravity and causality.