Integrating a single Fredkin (controlled swap) gate to the previously introduced W state fusion mechanism (Ozdemir et al, N. J. Phys. 13, 103003, 2011) and using an ancillary photon, we increase the size of the fused W states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic W state fusion mechanism. Besides fusing arbitrary size W states, our setup can also fuse Bell states to create W states with a success probability 3/4 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 W states. Since 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.When the number of particles forming an entangled state increases beyond two (i.e., two corresponding the bipartite case), a variety of states with more complex and different entanglement structures emerge. More interestingly, these states fall in inequivalent classes with Greenberger-Horne-Zeilinger (GHZ), W, Dicke and cluster states being the well-known examples. States belonging to different classes cannot be converted to each other even under stochastic local operations and classical communications (SLOCC) [2]. Understanding the entanglement structures and the formation of states belonging to different inequivalent classes is important not only for the general entanglement theory, but also for their vital roles in various quantum information processing tasks such as some quantum algorithms, quantum key distribution, quantum teleportation, measurement based quantum computation, etc. It is known that some states are more suitable for specific tasks than the others [3-10]. Thus, preparation of task-specific multipartite entangled states could benefit the quantum information science significantly. However, it is also crucial that these states are prepared using the resources efficiently with minimal costs. Therefore, simple and efficient schemes and methodologies to prepare large-scale multipartite entangled states are being sought, and there have been tremendous efforts put into this endeavour.Bipartite entangled states are understood very well. In principle, starting with EPR pairs, we can prepare arbitrary bipartite entangled states. We now know how to prepare, characterize, manipulate and use bipartite entangled states for specific tasks. We also know how to use EPR pairs as resources to prepare multipartite entangled states such as GHZ, W and cluster states [13][14][15][16][17][18][19][20][21]. However, despite the great efforts the theory and experiments on multipartite entanglement have been lagging. In the last decade, expansion and fusion operations are proposed and demonstrated as efficient ways of preparing large scale multipartite entangled states. In the expan- * Electronic address: MansurSah@gmail.com sion operation, the number of qubits in an entangled ...

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 − 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.

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In large quantum systems multipartite entanglement can be found in many inequivalent classes under local operations and classical communication. Preparing states of arbitrary size in different classes is important for performing a wide range of quantum protocols. W states, in particular, constitute a class with a variety of quantum networking protocols. However, all known schemes for preparing W states are probabilistic, with resource requirements increasing at least sub-exponentially. We propose a deterministic scheme for preparing W states that requires no prior entanglement and can be performed locally. We introduce an all-optical setup that can efficiently prepare W states of arbitrary size. Our scheme advances the use of W states in real-world quantum networks and could be extended to other physical systems.

We study the quantum Fisher information (QFI) of W states and W -like states under decoherence. In particular, we nd that on the contrary to amplitude damping and depolarizing decoherence, a W -like state of 3 qubits obtained by discarding 1 qubit of a genuine W state of 4 qubits is more robust than a genuine W state of 3 qubits under amplitude amplifying and phase damping decoherence.