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

TL;DR

This paper introduces two LOCC-based schemes for maximal entanglement concentration of a broad class of $(n+1)$-qubit states, achieving optimal success probability and feasible implementation in optical and solid-state systems.

Contribution

The paper presents novel entanglement concentration protocols applicable to various important multi-qubit states with maximum success probability of $2\beta^{2}$, including practical implementation methods.

Findings

Maximum success probability of $2\beta^{2}$ for the protocols.

Protocols applicable to Bell, GHZ, cluster, and other multi-qubit states.

Feasible implementation in optical, quantum dot, and microcavity systems.

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.