Quantum Action-Dependent Channels

We study communication over a quantum action-dependent channel, where the transmitter first performs an action that "shocks" the channel environment, and subsequently encodes a message into a transmission sent through the channel.

This two-stage interaction arises in various settings, including rewriting over defective memory and quantum effects such as measurement-induced state collapse.

Our model can be viewed as a quantum generalization of Weissman's classical action-dependent channel (2010).

Here, however, Alice cannot have a copy of the environment state due to the no-cloning theorem.

Instead, she may share entanglement with this environment.

We derive achievable rates for reliable message transmission via the quantum action-dependent channel, with either causal or non-causal channel side information (CSI).

As a case study, we analyze memory storage with depolarization and selective rewriting, demonstrating how action-dependent control influences performance.