Efficiencies of quantum optical detectors

We propose a definition for the efficiency that can be universally applied to all classes of quantum optical detectors. This definition is based on the maximum amount of optical loss that a physically plausible device can experience while still replicating the properties of a given detector. We prove that detector efficiency cannot be increased using linear optical processing. That is, given a set of detectors, as well as arbitrary linear optical elements and ancillary light sources, it is impossible to construct detection devices that would exhibit higher efficiencies than the initial set.

Figure 1

Equivalent loss model of detector. (a) An inefficient detector with POVM $\vec{\widehat{\Sigma }}$ and efficiency $\eta$ is equivalent to a detector with POVM $\vec{\widehat{\Pi }}$ preceded by an attenuator with transmissivity $\eta$. (b) An equivalent model of quantum state measurement with an imperfect detector.

Figure 2

A single-mode virtual detector. (a) Generalized model. The mode to be measured and the ancillary modes are processed by an interferometer and impinge onto the physical detectors, whose equivalent models are shown inside the dotted rectangles. (b) Equivalent model of the virtual detector. The input mode is subjected to immediate attenuation, which implies that the detector efficiency cannot exceed ${\eta }^{max}$.

Figure 3

A single-mode virtual detector with adaptive measurements for $M=7$. The virtual detector is again shown inside the dotted rectangle. The dotted lines from the detectors to the interferometers indicate that the interferometers are controlled based on the results of the detections.