Tomography of a feedback measurement with photon detection

Measurement and discrimination of quantum states are essential tasks in quantum information processing. A measurement strategy consisting of photon detection preceded by a displacement operation, that is actively feedback-controlled depending on the photon detection outcomes, is known to be a powerful measurement technique for quantum state discrimination [1] .

In our work, we experimentally develop such a feedback measurement with photon detection and characterize its positive operator valued measure (POVM) via quantum detector tomography using coherent states. Quantum detector tomography has been demonstrated for various types of static measurements [3] , but not before for a dynamically updated measurement.

As a potential application of the feedback measurement for quantum state discrimination, we analyze the performance of our measurement for the discrimination of the two orthogonal superpositions of vacuum and single photon states $| \pm \rangle = (|0\rangle \pm |1\rangle )/\sqrt 2 $ , which are the conjugate basis states of the optical single-rail qubit.