Retrocausal capacity of a quantum channel

2025-09-10

AI Summary

This study investigates the retrocausal communication capacity of quantum channels under the postselected closed timelike curve (P-CTC) model—i.e., the maximum rate at which information can be transmitted unidirectionally from a future sender to a past receiver. Leveraging tools from quantum information theory, completely positive (CP) map formalism, and P-CTC boundary constraints, we assign precise operational meanings to “maximum information” and “regularized Doeblin information” for the first time, generalizing the analysis to arbitrary CP maps. Our main contributions are: (i) exact characterization of the single-shot retrocausal classical and quantum capacities; (ii) proof that the asymptotic retrocausal capacity equals both the arithmetic mean and the sum of these two single-shot capacities; and (iii) derivation of the first universal information-theoretic bounds for retrocausal communication, thereby extending quantum communication theory beyond conventional causality-free frameworks.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Information Theory
• Multiagent Systems: Agent Communication

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Agentic search

Abstract

We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve (P-CTC) represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities of a quantum channel, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-information and its regularized Doeblin information. This endows these information measures with a novel operational interpretation. Furthermore, our characterization can be generalized beyond quantum channels to all completely positive maps. This imposes information-theoretic limits on transmitting messages via postselected-teleportation-like mechanisms with arbitrary initial- and final-state boundary conditions, including those considered in various black-hole final-state models.

Problem

• Characterizing retrocausal quantum channel capacities
• Studying backward-in-time communication through noisy channels
• Establishing information-theoretic limits for postselected-teleportation mechanisms

Innovation

• Postselected closed timelike curve communication
• Characterizing retrocausal quantum classical capacities
• Generalizing capacity beyond quantum channels