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Laser Physics

Fusion of W -like states in optical system

Ke Li, Ming Yang, Qing Yang, Zhuo‐Liang Cao

Published Jan 12, 2016• 6 citations
Publisher

Abstract

Abstract An effective scheme is proposed for preparing large-scale maximally entangled W states by fusing arbitrary-size polarization entangled W or W -like states via polarization-dependent beam splitter (PDBS). In our scheme, W m + n −1 state can be generated from an n -qubit W state and an m -qubit W state, and W m + n + t −2 state can be generated from W m , W n and W t states. The fusion process can start with Bell states too. Because PDBS has selective transmission rates for different polarization states, our fusion has a distinct property, i.e. a large-scale maximally entangled W state can be generated by fusing small-size W -like states, and the cost analyses indicate that our fusion scheme is more efficient than the previous one in fusing W -like states. In addition, there is no need for any controlled quantum gate and any ancillary photon in our scheme, so it is simple and feasible.

DOI
10.1088/1054-660x/26/2/025203

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Abstract An effective scheme is proposed for preparing large-scale maximally entangled W states by fusing arbitrary-size polarization entangled W or W -like states via polarization-dependent beam splitter (PDBS). In our scheme, W m + n −1 state can be generated from an n -qubit W state and an m -qubit W state, and W m + n + t −2 state can be generated from W m , W n and W t states. The fusion process can start with Bell states too. Because PDBS has selective transmission rates for different polarization states, our fusion has a distinct property, i.e. a large-scale maximally entangled W state can be generated by fusing small-size W -like states, and the cost analyses indicate that our fusion scheme is more efficient than the previous one in fusing W -like states. In addition, there is no need for any controlled quantum gate and any ancillary photon in our scheme, so it is simple and feasible.
With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled photonic W states into a large-scale W state without qubit loss, i.e.,Wn+m state can be generated from an n-qubit W state and a m-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 remaining states are recyclable. In addition, there is no need for any controlled quantum gate and any ancillary photon, so this fusion scheme may be implemented with current experimental techniques.
We propose an optical scheme to prepare large-scale entangled networks of WWW states. The scheme works by simultaneously fusing three polarization-encoded WWW states of arbitrary size via accessing only one qubit of each WWW state. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in S. K. Ozdemir et al., New J. Phys. 13, 103003 (2011)], and an HHH-polarized ancilla photon. Starting with three nnn-qubit WWW states, the scheme prepares a new WWW state with $3(n\ensuremath{-}1)$ qubits after postselection if both fusion gates operate successfully, i.e., a fourfold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large WWW states considerably when compared to previously reported schemes.
Abstract We present a qubit-loss-free (QLF) fusion scheme for generating large-scale atom W states in cavity quantum electrodynamics (QED) system. Compared to the most current fusion schemes which are conditioned on the case where one particle can be extracted from each initial W state to the fusion process, our scheme will access one or two particles from each W state. Based on the atom–cavity-field detuned interaction, three |W〉 n+m+t states can be generated from the |W〉 n , |W〉 m , and |W〉 t states with the help of two auxiliary atoms, and three |W〉 n+m+t+q states can be generated from |W〉 n , |W〉 m , |W〉 t , and a |W〉 q state with the help of three auxiliary atoms. Comparing the numerical simulations of the resource cost of fusing three small-size W states based on the previous schemes, our fusion scheme seems to be more efficient. This QLF fusion scheme can be generalized to the case of fusing k different or identical particle W states. Furthermore, with no qubit loss, it greatly reduces the number of fusion steps and prepares W states with larger particle numbers.
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.
We introduce a simple optical gate to fuse arbitrary-size polarization entangled W-states to prepare larger W-states. The gate requires a polarizing beam splitter (PBS), a half-wave plate (HWP) and two photon detectors. We study, numerically and analytically, the necessary resource consumption for preparing larger W-states by fusing smaller ones with the proposed fusion gate. We show analytically that resource requirement scales at most sub-exponentially with the increasing size of the state to be prepared. We numerically determine the resource cost for fusion without recycling where W-states of arbitrary size can be optimally prepared. Moreover, we introduce another strategy that is based on recycling and outperforms the optimal strategy for the non-recycling case.