Quantum Inf Process (2017) 16:26
Reﬁned entanglement concentration for electron-spin
entangled cluster states with quantum-dot spins in
· Gui-Lu Long
Received: 20 September 2016 / Accepted: 7 December 2016 / Published online: 19 December 2016
© Springer Science+Business Media New York 2016
Abstract We presenta reﬁned entanglementconcentration protocol (ECP)for an arbi-
trary unknown less-entangled four-electron-spin cluster state by exploring the optical
selection rules derived from the quantum-dot spins in one-sided optical microcavities.
In our ECP, the parties obtain not only the four-electron-spin systems in the partial
entanglement with two unknown parameters, but also the less-entangled two-electron-
spin systems in the ﬁrst step. Utilizing the above preserved systems as the resource for
the second step of our ECP, the parties can obtain a standard cluster state by keeping
the robust odd-parity instances with two parity-check gates. Meanwhile, the systems
in the rest three instances can be used as the resource in the next round of our ECP.
The success probability of our ECP is largely increased by iteration of the ECP pro-
cess. Moreover, all the coefﬁcients of our ECP are unknown for the parties without
assistance of extra single electron-spin, so our ECP maybe has good applications in
quantum communication network in the future.
Keywords Entanglement concentration · Electron-spin · Cluster state · One-side
State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,
Tsinghua University, Beijing 100084, China
Tsinghua National Laboratory of Information Science and Technology, Beijing 100084, China
Collaborative Innovation Center of Quantum Matter, Beijing 100084, China