Retrocausal capacity of a quantum channel
This work provides a foundational information-theoretic framework for retrocausal communication, with implications for quantum information theory and black-hole physics.
The paper characterizes the one-shot and asymptotic capacities of a quantum channel for retrocausal communication via a postselected closed timelike curve, showing they equal the average and sum of the channel's max-information and regularized Doeblin information, providing an operational interpretation for these measures.
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) mathematically represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities, 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.