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Preparation and Local Manipulation of Photonic W States Using Expansion and Fusion Gates

Şahin Kaya Özdemir, Toshiyuki Tashima, Takashi Yamamoto, Masato Koashi, Nobuyuki Imoto

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We report experimental demonstration of an optical gate that increases the size of polarization-entangled W-states by accessing only one qubit, and discuss strategies of local expansion and fusion to prepare large scale W-state networks.
DOI
10.1364/qels.2011.qtht2

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We demonstrate an optical gate that increases the size of polarization-based W states by accessing only one of the qubits. Using this gate, we have generated three-photon and four-photon W states with fidelities 0.836 ± 0.042 and 0.784 ± 0.028, respectively. We also confirmed the existence of pairwise entanglement in every pair of qubits, including the one that was left untouched by the gate. The gate is applicable to any size of W states and hence is a universal tool for expanding entanglement.
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 introduce a nonunitary partial-swap gate for fusing arbitrary small-sized photonic W-states into a large-scale entangled network of W-state efficiently without ancillary photons. A partial-swap gate is designed in an optical architecture based on linear optics elements. By introducing auxiliary degree of freedom, this gate provides a higher success probability with less cost. Our implementation can create a larger target state with a simpler set-up than previous proposals for W-state fusion. Also all ‘garbage’ states are recyclable, i.e., there is no complete failure output in our scheme in principle.
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.