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Optics Communications

One-photon controlled two-photon not gate contributed by weak cross-Kerr nonlinearities

Xiao‐Ming Xiu, Qing-Yang Li, Yan-Fang Lin, Li Dong, Haikuan Dong, Yajun Gao

Published Feb 23, 2017• 6 citations
Publisher
DOI
10.1016/j.optcom.2017.02.051

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With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled W states into a large-scale W state without qubit loss, i.e.,Wn+m\mathrm{W}_{n+m}Wn+m​ state can be generated from an nnn-qubit W state and a mmm-qubit W state. To complete the fusion task, two polarization entanglement processes and one spatial entanglement process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. We analyze the resource cost and the success probability of the scheme. There is no complete failure output in our fusion mechanism, and all the garbage states are recyclable. In addition, there is no need for any controlled quantum gate and any ancillary photon, so it is simple and feasible under the current experiment technology.
Abstract By harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.