Deterministic generation of a four-qubit W state using one- and two-qubit gates

Abstract

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.