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AIP conference proceedings

Local transformation of two EPR photon pairs into a three-photon W state

Toshiyuki Tashima, T. Wakatsuki, Şahin Kaya Özdemir, Takashi Yamamoto, Masato Koashi, N. Imoto, Alexander I. Lvovsky

Published Jan 1, 2009• 3 citations
Publisher

Abstract

We propose and demonstrate a local transformation of two EPR photon pairs to three‐photon W state. The key issue of our scheme is that it requires only one polarization dependent beamsplitter to perform the necessary local operation. Using a quantum state tomography, the fidelity of the prepared three‐photon state was estimated as 0.778±0.043. The expectation value of the witness operator of W3 was −0.111±0.043.

DOI
10.1063/1.3131313

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We propose and demonstrate a local transformation of two EPR photon pairs to three‐photon W state. The key issue of our scheme is that it requires only one polarization dependent beamsplitter to perform the necessary local operation. Using a quantum state tomography, the fidelity of the prepared three‐photon state was estimated as 0.778±0.043. The expectation value of the witness operator of W3 was −0.111±0.043.
We propose and experimentally demonstrate a transformation of two Einstein-Podolsky-Rosen photon pairs distributed among three parties into a three-photon W state using local operations and classical communication. We then characterize the final state using quantum state tomography on the three-photon state and on its marginal bipartite states. The fidelity of the final state to the ideal W state is 0.778+/-0.043 and the expectation value for its witness operator is -0.111+/-0.043 implying the success of the proposed local transformation.
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.
A system of two polarized photons in singlet state appears as being in one of two product states independent of any measurement. These states depend on the selected polarization angles. With the polarizers on either side perpendicular to each other, both photons pass the polarizers without any disturbance. Action at a distance is therefore not needed to explain the results of the measurements. In general, the elements of physical reality demanded by EPR are the polarization states of the two photons of the entangled pair. As these are local elements in the regions of space of the polarizers the EPR paradox for the case of entangled photons can be regarded as resolved.