Unambiguous state discrimination as a limit of an optimal nonprojective measurement of binary coherent states

Recent advances in quantum measurement theory have shown that it is possible to realize an optimal inconclusive measurement of binary nonorthogonal coherent states based on linear optics, coherent displacement operations, continuous photon counting, and fast feedback [1]. The optimal inconclusive measurement is a nonprojective quantum measurement that generalizes the minimum error (Helstrom) measurement and the optimal unambiguous measurement of binary states, achieving the minimum error probability for a given probability of an inconclusive result. We study this optimal nonprojective measurement to implement the zero-error optimal unambiguous state discrimination (USD) of binary coherent states. While it is possible to implement optimal USD of binary coherent states with a measurement based on displacement operations to the vacuum state without feedback [2], it is known that such an optimal quantum measurement cannot be implemented in the presence of experimental imperfections due to the impossibility of perfectly realizing this displacement operation. We explore the use of the optimal inconclusive measurement in this zero-error regime, which does not fully rely on displacement operations to the vacuum state, with the aim of demonstrating a USD measurement that is more robust to experimental imperfections. This robust quantum measurement can be critical in realistic implementations of quantum communication protocols based on USD of coherent states.

[1] K. Nakahira and T. S. Usuda, Phys. Rev. A 86, 052323 (2012).

[2] K. Banaszek, Phys. Lett. A 253, 12 (1999).