Indefinite Causal Order and Quantum Coordinates

Area of Science:

• Quantum physics
• General relativity
• Causality

Background:

• Classical physics dictates a fixed causal order for events.
• Quantum mechanics permits superpositions of causal orders, exemplified by the quantum switch.
• Debate exists on whether optical quantum switches truly represent indefinite causal order or merely simulate it.

Purpose of the Study:

• To provide a relativistic definition of causal order.
• To establish a meaningful observable for causal order in both general relativistic and quantum mechanical contexts.
• To resolve the debate on the validity of optical quantum switch experiments.

Main Methods:

• Developed a relativistic definition of causal order.
• Defined an observable for causal order based on operationally defined events.
• Compared the observable across different quantum switch implementations.

Main Results:

• The defined observable is meaningful in both general relativistic and quantum mechanical frameworks.
• The observable does not differentiate between optical quantum switches and hypothetical gravitational quantum switches.
• This supports the physical reality of indefinite causal order in current experiments.

Conclusions:

• Optical quantum switch experiments are valid realizations of indefinite causal order.
• A superposition of spacetime metrics is not strictly required for indefinite causal order.
• The findings bridge quantum mechanics and general relativity concerning causality.