Preparation of a three-photon W state from two EPR photon pairs by LOCC

In quantum information science, it is often the question what distantly located parties sharing EPR pairs can achieve if they are restricted to only local operations and classical communication (LOCC). State preparation and transformation is one of such tasks, which have been attracted considerable interest since the early years of the field. It is well-known that starting with EPR pairs, any two-qubit pure state can be prepared via only LOCC. Thus EPR pairs form a universal resource. However, the situation is very different when the multipartite entanglement is considered, because in multipartite entanglement, there are distinct classes of entanglement, which cannot be converted into each other with unit fidelity even under stochastic local operation and classical communication (SLOCC), e.g., two distinct classes of states, GHZ-type and W-type states for the tripartite cases [1]. There exists no tripartite state that can be used as a universal resource to generate arbitrary tripartite pure states using SLOCC. For this purpose, one must look for a resource in larger systems such as many shared EPR pairs to extract the desired multipartite state. For example, there is a direct way of converting two EPR pairs into a three-qubit GHZ-type state [2], which then can be used to prepare approximate W state [3]. In this conversion from GHZ to W state, there is a trade-off between the fidelity and success probability. Unit fidelity cannot be achieved with non-zero probability, which confirms that GHZ- and W-type states belong to distinct classes.