Multiple-copy State Discrimination of Noisy Qubits

Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, nonorthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability of successful discrimination allowed by quantum theory. For mixed states, it is known that only collective schemes can perform optimally, so it might be expected that these schemes are more resilient to preparation noise. We calculate the probability of success for two schemes, a local scheme based on Bayesian updating and quantum data gathering, the simplest possible collective measurement, and consider imperfect preparation fidelity. We find two surprising results. First, both schemes converge upon the same many-copy limit, which is less than unity. Second, the local scheme performs better in all cases. This highlights the point that one should take into account noise when designing state discrimination schemes.