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arXiv:0803.1897 · Physical Review A

Elementary optical gate for expanding an entanglement web

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

Published Mar 25, 2008• 90 citations
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Abstract

We introduce an elementary optical gate for expanding polarization entangled $W$ states in which every pair of photons is entangled alike. The gate is composed of a pair of 50:50 beamsplitters and ancillary photons in the two-photon Fock state. By seeding one of the photons in an $n$-photon $W$ state into this gate, we obtain an $(n+2)$-photon $W$ state after postselection. This gate gives a better efficiency and a simpler implementation than previous proposals for $W$-state preparation.

DOI
10.1103/physreva.77.030302

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We introduce an elementary optical gate for expanding polarization entangled WWW states in which every pair of photons is entangled alike. The gate is composed of a pair of 50:50 beamsplitters and ancillary photons in the two-photon Fock state. By seeding one of the photons in an nnn-photon WWW state into this gate, we obtain an (n+2)(n+2)(n+2)-photon WWW state after postselection. This gate gives a better efficiency and a simpler implementation than previous proposals for WWW-state preparation.
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.
We propose an optical scheme to build an entangled network composed of W state based on polarization encoded qubits (photons). This new setup consists of 2 cNOT gates, 4 V gates, 2 Hadamard gates and basic optical tools such as polarizing beamsplitters (PBSs) and path couplers (PCs). V gate is a specially-designed tool acting as a two-qubit gate which is composed of a cNOT gate, 3 PBSs and a PC. By using this gate, one benefits from the temporarily generated optical degree of freedom, which is the spatial mode of a photon in the proposed scheme. Using an extra degree of freedom allows us to perform more capable processing for W-state creation protocols. We use four photons as input, which means we do not need entanglement as a resource. Also, we show that the proposed scheme can be implemented by operating the quantum optical gates which can be realized via current photonics technology. Additionally, we provide discussions of quantum contextuality and non-locality for W states.
A simple scheme is proposed to implement a two-qubit linear optical quantum iSWAP gate that is a universal gate in quantum computation and quantum information processing. By the interference effect of the polarized photons, a quantum iSWAP gate can be achieved with a low success probability (η4/32, with η being the quantum efficiency of photon detectors). The scheme is based only on simple linear optical elements, a pair of two-photon polarization entangled states, and conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states, which greatly decreases the experimental difficulty of implementing linear optical quantum computation.