Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time

Abstract

There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time-reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with space-like separated input-output pairs. We explicitly describe a non-signaling device which becomes a perfect signaling device under time-reversal, where time-reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although time-reversal of Popuscu-Roerlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time-reversal using post-selection, which could lead experimental implementation.

4 pages, some figures; replaces arXiv:1010.4572 [quant-ph]

References in corpus (3)

• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Closed timelike curves via post-selection: theory and experimental demonstration
• Picturing classical and quantum Bayesian inference

Cited by in corpus (9)

• Beyond Bell's Theorem: Correlation Scenarios
• Operational quantum theory without predefined time
• Operational formulation of time reversal in quantum theory
• Terminality implies non-signalling
• Symmetries of quantum evolutions
• The Sheaf-Theoretic Structure of Definite Causality
• Time Symmetry in Operational Theories
• Relativistic Causality vs. No-Signaling as the limiting paradigm for correlations in physical theories
• Causality in Higher Order Process Theories