Quantum bounds and structured receiver performance for discriminating mixed states generated by weak measurement and thermal noise

Optimally discriminating between non-orthogonal states is critical to both quantum communications and quantum computation. As such, much work focuses on finding quantum bounds for minimal error discrimination and then comparing these quantum bounds with the performance of structured receivers. Pure state discrimination is well understood but deriving experimental strategies for discriminating mixed states has been less explored. We compute quantum bounds and receiver performance for discriminating between mixed states prepared by a pure coherent state mixed with thermal noise light in a channel and the same pure coherent state subject to weak measurement in a channel. We calculate the Helstrom bound for the case where a single copy of the quantum state is available for measurement and the quantum Chernoff bound, where copies of the quantum state occupy many modes and can be measured individually or with a joint measurement. We then compare these quantum bounds with the performance of different structured detection schemes, including direct and homodyne detection. The results have utility in quantum authentication, by enabling discrimination between a case of an attacker in a quantum key distribution system with weak measurement capabilities versus thermal noise in the channel.