Quantum State Discrimination with Prior Knowledge in Noisy Quantum Channels

Discrimination between two states of a qubit is investigated, which is performed under the influence of noisy quantum channels. When prior knowledge about on the quantum states is available, the detection probability of quantum measurement is compared with that of pure guessing during the irreversible time evolution. In the case of a Markovian channel, the superiority of quantum measurement to pure guessing is lost at finite time which is determined by the prior probability and the fidelity of the quantum states. For a non-Markovian channel, however, it is possible to recover the superiority of quantum measurement even if it is lost. The effect of a system-environment initial correlation on the quantum state discrimination is also investigated.