Passive scheme with a photon-number-resolving detector for monitoring the untrusted source in a plug-and-play quantum-key-distribution system

A passive scheme with a beam splitter and a photon-number-resolving (PNR) detector is proposed to verify the photon statistics of an untrusted source in a plug-and-play quantum-key-distribution system by applying a three-intensity decoy-state protocol. The practical issues due to statistical fluctuation and detection noise are analyzed. The simulation results show that the scheme can work efficiently when the total number of optical pulses sent from Alice to Bob is above 10^8, and the dark count rate of the PNR detector is below 0.5 counts/pulse, which is realizable with current techniques. Furthermore, we propose a practical realization of the PNR detector with a variable optical attenuator combined with a threshold detector.Comment: 8 pages, 6 figure

O-operators on associative algebras and associative Yang–Baxter equations

An O-operator on an associative algebra is a generalization of a Rota–Baxter operator that plays an important role in the Hopf algebra approach of Connes and Kreimer to the renormalization of quantum field theory. It is also the associative analog of an O-operator on a Lie algebra in the study of the classical Yang–Baxter equation. We introduce the concept of an extended O-operator on an associative algebra whose Lie algebra analog has been applied to generalized Lax pairs and PostLie algebras. We study algebraic structures coming from extended O-operators. Continuing the work of Aguiar deriving Rota–Baxter operators from the associative Yang–Baxter equation, we show that its solutions correspond to extended O-operators through a duality. We also establish a relationship of extended O-operators with the generalized associative Yang–Baxter equation