Optical Realization of Optimal Unambiguous Discrimination for Pure and Mixed Quantum States

Quantum mechanics forbids deterministic discrimination among nonorthogonal states. Nonetheless, the capability to distinguish nonorthogonal states unambiguously is an important primitive in quantum information processing. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three nonorthogonal states, with a success rate of 55%, to be compared with the 25% maximum achievable using projective measurements. Furthermore, we present the first realization of unambiguous discrimination between a pure state and a nonorthogonal mixed state.

Figure 1

(a) Eight-port optical interferometer: suitable beam splitters are placed at each crossing of two optical rails to realize any desired unitary transformation on the input states. A detection in rail 4 corresponds to an inconclusive result and a detection in rails 1 to 3 corresponds to states $|{\psi }_1⟩$ to $|{\psi }_3⟩$. (b) Experimental layout: this interferometer can perform various desired generalized measurement by doing arbitrary unitary operations in four-dimensional Hilbert space and projective measurements at output ports 1 to 4. The variable beam splitters (VBS) realize the corresponding beam splitters in (a) for arbitrary reflectivity and transmissions. Photodiodes PD1 to PD4 detect the photons at the output ports 1 to 4.

Figure 2

Experimental data: the results of state discrimination and of state filtering for the cases of $a=0.25$ and $a=0.5$, respectively, are presented in parts (a), (b), and (c). Each row corresponds to preparation of a pure or a mixed quantum state. The last column in each figure represents the inconclusive outcomes. The diagonal and off-diagonal elements of other columns represent the successful and erroneous detections, respectively. The probability of each outcome is a measure of the fraction of photons reaching the corresponding detector.