Linear-Optical Implementation of Perfect Discrimination between Single-bit Unitary Operations

For quantum computing and quantum information processing, one important task is the discrimination of quantum states and unitary operations. This is strongly related to quantum nonorthogonality, which is one of the basic features of quantum mechanics. Since the pioneering work of Helstrom [1] on quantum hypothesis testing, the problem of discriminating nonorthogonal quantum states has attracted much attention, both in theory [2, 3] and experiment [4, 5, 6, 7, 8]. Naturally, the concepts of nonorthogonality and distinguishability can also be applied to quantum operations. However, things become very different when we refer to quantum operations. Some pioneering works have been devoted to a good understanding of the exact role of quantum entanglement in the discrimination between unitary operations. It was proved [9, 10] that perfect discrimination of nonorthogonal unitary operations can always be achieved with a finite number of running the unknown unitary operation, by using a suitable entangled state as input. This is in contrary to the case of nonorthogonal quantum states, for which perfect discrimination can not be achieved with finite number of copies. Recently, Runyao Duan et al indicated that entanglement is not necessary for discrimination between unitary operations [11]. They show that by taking a suitable state and proper auxiliary unitary operation, nonorthogonal unitary operations can also be perfectly discriminated even without entanglement. This result impacts on the role of quantum entanglement in the context of quantum computing [12], and also makes experiment of discrimination much easier because no N -partite entangled state is needed. In this paper, we report an experiment which demonstrates perfect discrimination between single-qubit unitary operations in two ways (parallel and sequential). Linear optical elements are used to perform unitary operations on photonic qubits in the experiment. And entangled input states needed for parallel scheme are provided by spontaneous parametric down-conversion (SPDC) twin-photon source. The quality of our discriminating operation is characterized by the fidelity between output states. F (ρ 1 , ρ 2 ) ≡ Tr √