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Nonclassicality of Temporal Correlations.

Stephen Brierley1, Adrian Kosowski2, Marcin Markiewicz3

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This study introduces a new formulation of Bell's theorem for temporal correlations, defining nonclassical temporal correlations. It demonstrates that certain quantum temporal correlations, unlike classical ones, cannot be simulated by classical systems.

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Area of Science:

  • Quantum Information Science
  • Foundations of Quantum Mechanics
  • Quantum Correlations

Background:

  • Spacelike separated measurements exhibit two-way no-signaling, ensuring independence between distant measurement settings and outcomes.
  • Timelike separated measurements are only one-way no-signaling, where the past influences the future, but not vice versa.
  • This asymmetry allows some temporal correlations, despite formal similarity to nonclassical spatial correlations, to be classically modeled.

Purpose of the Study:

  • To propose a novel formulation of Bell's theorem tailored for temporal correlations.
  • To define nonclassical temporal correlations as those irreducible to classical information propagation over time.
  • To investigate the classical simulability of temporal correlations arising from quantum measurements.

Main Methods:

  • Defining nonclassical temporal correlations based on the inability to simulate them using classical information propagation bounded by the Holevo capacity.
  • Analyzing temporal correlations from projective quantum measurements on a single qubit.
  • Examining temporal correlations from general quantum measurements on an m-level quantum system.

Main Results:

  • Temporal correlations from any projective quantum measurements on a qubit are shown to be classically simulable.
  • A class of general measurements on an m-level quantum system is presented whose temporal correlations defy classical simulation, even with unlimited classical memory.
  • This highlights a distinction between classical and quantum temporal correlations beyond simple no-signaling principles.

Conclusions:

  • Not all temporal correlations in quantum mechanics are classically simulable, challenging classical intuition about time and information.
  • The proposed framework provides a new criterion for identifying genuine quantum correlations in the temporal domain.
  • The findings suggest limitations of classical computation and information propagation in fully capturing quantum phenomena evolving in time.