Fusion technique plays a key role in the preparation of large-scale $W$ states, but the currently existing fusion schemes are suffering from the qubit loss problem, i.e., the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories. In this paper, we design a fusion mechanism to fuse two small-size $W$ states into a large-scale $W$ state without qubit loss, and thus we call it qubit-loss-free (QLF) fusion mechanism. This QLF fusion mechanism is based on a two-outcome positive-operator valued measurement on two qubits extracting from two small-size $W$ states, and works for both pure and mixed $W$ states. The QLF nature of this fusion mechanism clearly increases the final size of the obtained $W$ state, and greatly reduces the number of fusion steps as well as the requirement of quantum memories required to achieve a $W$ state of a target size, so it is more efficient and feasible than the currently existing fusion schemes. There is no complete failure output in our QLF fusion scheme, and all the garbage states are recyclable. Two example schemes are proposed to realize this QLF fusion mechanism in a cavity quantum electrodynamics system and three-qubit Heisenberg XYZ model, respectively, which demonstrates the possibility of the physical realization of this QLF fusion mechanism.

• Received 26 September 2016

DOI:https://doi.org/10.1103/PhysRevA.94.062315