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arXiv:1402.3152 · Physical Review A

Fusing multiple W states simultaneously with a Fredkin gate

Fatih Özaydin, Sinan Bugu, Can Yesilyurt, Azmi Ali Altıntaṣ, Mark Tame, Şahin Kaya Özdemir

Published Apr 14, 2014• 89 citations
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Abstract

We propose an optical scheme to prepare large-scale entangled networks of $W$ states. The scheme works by simultaneously fusing three polarization-encoded $W$ states of arbitrary size via accessing only one qubit of each $W$ 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 $H$-polarized ancilla photon. Starting with three $n$-qubit $W$ states, the scheme prepares a new $W$ 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 $W$ states considerably when compared to previously reported schemes.

DOI
10.1103/physreva.89.042311

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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)3(n\ensuremath{-}1)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.
Integrating a single Fredkin (controlled swap) gate to the previously introduced WWW state fusion mechanism [Ozdemir et al., New J. Phys. 13, 103003 (2011)] and using an ancillary photon, we increase the size of the fused WWW states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic WWW-state fusion mechanism. Besides fusing arbitrary size WWW states, our setup can also fuse Bell states to create WWW states with a success probability 3/43/43/4 which is much higher than the previous works. Therefore using only this setup, it is now possible to start with Bell pairs to create and expand arbitrary size WWW states. Since a higher probability of success implies a lower cost of resource in terms of the number of the states spent to achieve a target size, our setup gives rise to more cost-efficient scenarios.
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.
Creation of large-scale W state quantum networks is a key step for realization of various quantum information tasks.Regarding the photonics technology, a simple optical setup was proposed for the fusion of two W states.Recently it was shown that via a single Fredkin gate, this basic so-called fusion setup can be enhanced.However the main problem was that the probability of success of realization of Fredkin gate with linear optics is too low.In this work, we show that the same enhancement can be made possible via one Tooli and one CNOT gate, instead of a Fredkin gate.Not only the probability of success of the combination of these two gates is much higher, than that of a single Fredkin gate via linear optics, but also there is another method for implementing our setup with current photonics technology, almost with a unity success probability: A hybrid circuit consisting of a Tooli gate which can be implemented via one-way quantum computation on a weighted graph state of 8 qubits with a unity success probability and a linear optical CNOT gate which has a success probability close to unity.Therefore the preparation of polarization based encoded multi particle entangled W states of arbitrary sizes becomes considerably more ecient.
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.
Abstract Qubit-loss-free fusion for two W states introduced by Li K et al (2016 Phys. Rev . A 94 062315) clearly increases the final size of the obtained W state and greatly reduces the number of fusion steps to achieve a W state of a target size. Motivated by this idea, we propose a qubit-loss-free fusion scheme for fusing three polarization entangled W states simultaneously. The elements of a two-outcome positive-operator valued measurement and the appropriate joint unitary operation for realizing a positive-operator valued measurement measurement are given. As an example, with the assistance of weak cross-Kerr nonlinearities, an optical setup for fusing three W states is proposed. We analyze the success probability of the scheme and the resource cost of the present scheme, as compared to previous work.