Improving single photon sources via linear optics and photodetection

Abstract

Triggered single-photon sources produce the vacuum state with nonzero probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states with probabilities 1 − p and p, respectively. Here we are concerned with increasing the efficiency p by directing multiple copies of the single-photon-vacuum mixture into a linear optical device and applying photodetection on some outputs. We prove that it is impossible, under certain conditions, to increase p via linear optics and conditional preparation based on photodetection. We also establish a class of photodetection events for which p can be improved, although with an added multiphoton component. In addition we prove that it is not possible to obtain perfect single-photon states via this method from imperfect ͑p Ͻ 1͒ inputs. . Although these sources do not have as high a fidelity as can be achieved using parametric downconversion [4], they have the advantage that they are triggered. For a triggered single-photon source, the probability of more than one photon being produced is much lower than that for a Poissonian process [10], but the vacuum contribution can be quite high. That is, the coefficients q n of the single-mode output field density matrix ͚ n q n ͉n͗͘n͉ are negligible for n ജ 2, but the vacuum contribution q 0 is substantial. For this study we consider an ideal single-mode singlephoton source with limited efficiency p, which may be represented by the density operatorIncreasing the efficiency p is important because of requirements for quantum optics experiments, especially those concerned with quantum information processing. Much of this effort is directed to improving sources, but here we pose the question as to whether it is possible to perform postprocessing to obtain higher efficiency, while maintaining a negligible multiphoton contribution. A promising method of postprocessing is via linear optics and photodetection. It has been shown that linear optics and photodetection can be used to perform quantum computation ͓2͔, and optical controlled- NOT Below we show that it is impossible to increase the single-photon efficiency p, provided we consider detection results where all but one of the photons are detected. This eliminates the most straightforward possibility for ensuring that the multiphoton contribution is negligible. If we allow other detection results, we show it is possible for lowefficiency (small p) single-photon states to yield, via linear optics and conditional preparation based on photodetection, an output with a larger probability for a single photon. However, these schemes also yield multiphoton contributions comparable to the Poisson distribution.In the general case we start with a supply of N mixed states of the form (1). For additional generality we allow the different inputs to have different probabilities for a single photon, p i , and we denote the maximum of these probabilities by p max . The initial input stat...

Journeys from quantum optics to quantum technology

“…Motivated by the post-selected nonlinear-sign gate for linear-optical quantum computation [248], Peter Knight, I and others collaborated on improving triggered single-photon source efficiency, i.e., the probability for a single photon to appear in a pulse instead of vacuum, while avoiding multiphoton pulses. We established no-go results for enhancing efficiency via linear optics and conditional preparation based on photodetection [249,250]. Our work focused on reducing the general question of whether improving single-photon sources in this way could be reduced to a simple case from which all general results would follow.…”

Efficiency limits for linear optical processing of single photons and single-rail qubits

“…1: General processing of multiple SRQs or single-photon sources. [6,7]. Numerical results in support of the conjecture are presented in Sec.…”

“…A range of examples are presented in Appendix VII. A notable feature of these schemes is that they use resources such as coherent states and general projective measurements for the processing; these resources were not considered in earlier work on processing single-photon sources [6,7]. Here we examine general processing including these resources, and show that all the results found for more restricted processing also hold when we allow coherent states and general measurements.…”

“…VI; here we restrict these inputs to be inefficient single-photon sources. We consider a more general form of processing than that in previous work [6,7], and allow coherent state inputs and general measurements on the outputs. We have N 1 single-photon sources with efficiencies p i , and N − N 1 coherent states |α N1+1 , .…”

“…The possibility of such an improvement was investigated by Berry and co-workers [6,7], who considered a general interferometric circuit with N inefficient single photons as inputs. All output modes except one were subject to photon number measurements, and the quantum state of the remaining mode, conditioned on a particular result of this measurement, was analyzed.…”