Photodetector figures of merit in terms of POVMs

Abstract

A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement device is fully described by its positive-operatorvalued measure (POVM) which generalizes the textbook notion of the eigenstates of the appropriate hermitian operator (the 'observable') as measurement outcomes. Here we show how to define a multitude of photodetector figures of merit in terms of a given POVM. We distinguish classical and quantum figures of merit and issue a conjecture regarding trade-off relations between them. We discuss the relationship between POVM elements and photodetector clicks, and how models of photodetectors may be tested by measuring either POVM elements or figures of merit. Finally, the POVM is advertised as a platform-independent way of comparing different types of photodetectors, since any such POVM refers to the Hilbert space of the incoming light, and not to any Hilbert space internal to the detector.

Detecting two photons with one molecule

“…(where we ignored an exponentially small term in the second line) is that of a bandwidth: the effective size of the single-photon Hilbert space covered by this particular measurement outcome [18]. This bandwidth may be (much) larger than unity.…”

“…To construct the minimal absorber atom or molecule or multi-level system that can absorb two photons sequentially and produce classical outputs signaling the final state of the absorber, we consider the five level system of Figure 1 for efficient photon transduction. Some recent efforts for physically based fundamental models for photo detection assemble all parts of the process into a single fully coupled evolution problem [13,14,[18][19][20][21][22][23][24]. Minimal noise amplification of the absorbed photon signal has been shown to be optimally done with continuous quantum measurement [13,14,23].…”

“…One motivation for this work comes from recent theory efforts to find fundamental (i.e., device-independent) limits to photo detection [13,14,[18][19][20][21][22][23][24]. For reasons fully explained in [23] we construct a Hamiltonian here for the full detection process, including the crucial amplification step.…”

Quantum networks for single photon detection

“…Critically, knowing T (ω) for a specific photo detector also allows one to construct the positive-operator valued measure (POVM), from which all standard figures of merit can be obtained [38]. The POVM element corresponding to a click after the photo detector has been left on for a very long time (in particular, long compared to the bandwidth τ Γ −1 ; see Appendix A for a detailed POVM construction) has the particularly simple form…”

“…[71] The uncertainty in frequency, as defined in [38] and calculated entropically from the spectral POVM [34], is in this case directly proportional to the bandwidth (and hence also independent of discrete state spacing).…”