Quantum state discrimination is a fundamental task in quantum information theory and also an important building block in practical quantum information applications. We here consider optimal state discrimination in a noisy environment in which quantum states may be corrupted due to the intervention of an environment. We show that even if there exists an unwanted interaction with an environment and the channel describing the interaction is not yet identified, a measurement prepared in the beginning for optimal state discrimination can be preserved as an optimal measurement ever after a channel use. This means that in a practical realization of quantum communication, verification of a channel can be circumvented and the cost of quantum tomography is saved. We also show a protocol of preserving an optimal measurement for state discrimination.
We develop a state discrimination approach to unassisted quantum communication through a noisy quantum channel. Starting from the operational duality between entanglement recovery and state discrimination, we construct entanglement-generation codes with explicit decoders constructed from Petz recovery maps. The resulting error bounds hold for every number of channel uses and are expressed in terms of Petz-Rényi coherent information. For product sources, they yield exponential error decay at rates below coherent information.