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We introduce a new tool, the circuit (super)operator, to study quantum processes with undefined causal order. This framework reveals that different "causal perspectives" of a quantum switch are not interchangeable descriptions.

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Area of Science:

  • Quantum Information Science
  • Foundations of Quantum Mechanics
  • Quantum Causality

Background:

  • Cyclic quantum operations can challenge the standard notion of causal order.
  • Quantum systems delocalized in time can realize processes with indefinite causality.

Purpose of the Study:

  • Introduce the circuit (super)operator for analyzing quantum circuits under changing subsystem decompositions.
  • Investigate the relationship between causally indefinite processes and their temporal realizations.
  • Apply the framework to the quantum switch to understand different causal perspectives.

Main Methods:

  • Development of the circuit (super)operator formalism.
  • Analysis of quantum circuits and their transformations.
  • Application to the quantum switch model.

Main Results:

  • The circuit (super)operator unifies the study of cyclic quantum circuits and causal indefiniteness.
  • Two distinct temporal realizations of the quantum switch are identified as "causal perspectives."
  • These causal perspectives are shown to be fundamentally distinct and not transformable into one another via subsystem decomposition.

Conclusions:

  • The circuit (super)operator provides a powerful tool for exploring quantum causality.
  • Causal perspectives in quantum mechanics are not always equivalent descriptions of the same underlying process.
  • This work has implications for understanding quantum computation and the nature of time in quantum theory.