We answer Mandel's comments on a model of photon counting which we proposed earlier, by showing how it may be applied to some typical open systems. We also clarify the circumstances under which Mandel's formula is quantitatively indistinguishable from ours.
We reconsider various approaches to the quantum theory of photodetection from the point of view of the quantum theory of measurement, and show that important differences between them depend upon the manner in which they take into account the modification of the field distribution produced by the presence of the detector. We show that the Mandel photon counting formula may lead to unphysical results, such as negative probabilities, in some situations just because this modification is not incorporated into the model. We also show that the recently developed quantum theory of continuous measurements provides a completely satisfactory framework for discussing photon counting experiments. As an illustration, an exact derivation of the photon statistics of a single-mode free field is presented, and some of the results are shown to be identical to those derived earlier by Mollow and others. We also indicate how our approach can be extended to discuss the photon statistics of fields in interaction with sources and reservoirs.
Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity Find of an N-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on Find. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of Find for arbitrary N-photon states. Both protocols can certify Find=1−O(ε) using provably optimal O(1/ε) samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.