Maximal entanglement concentration for $(n+1)$-qubit states

Abstract

We propose two schemes for concentration of $(n+1)$-qubit entangled states that can be written in the form of $(\alpha|\varphi_{0}\rangle|0\rangle+\beta|\varphi_{1}\rangle|1\rangle)_{n+1}$ where $|\varphi_{0}\rangle$ and $|\varphi_{1}\rangle$ are mutually orthogonal $n$-qubit states. The importance of this general form is that the entangled states like Bell, cat, GHZ, GHZ-like, $|\Omega\rangle$, $|Q_{5}\rangle$, 4-qubit cluster states and specific states from the 9 SLOCC-nonequivalent families of 4-qubit entangled states can be expressed in this form. The proposed entanglement concentration protocol is based on the local operations and classical communications (LOCC). It is shown that the maximum success probability for ECP using quantum nondemolition (QND) technique is $2\beta^{2}$ for $(n+1)$-qubit states of the prescribed form. It is shown that the proposed schemes can be implemented optically. Further it is also noted that the proposed schemes can be implemented using quantum dot and microcavity systems.