˖ڍመڙጲ
http://www.pap er.edu.cn
increase distance, such as quantum repeater [33, 34], quantum error correction code (QECC)
[35], entanglement purification [36, 37], decoherence-free subspace (DFS) [38, 39, 40, 41, 42, 43]
and so on. Entanglement concentration is also an effective way to preserve the fidelity of en-
tangled channels which is employed to distill maximally entangled states from an ensemble of
partially entangled pure state [44]. Many kinds of entanglement concentration schemes has
been proposed and discussed based on different quantum state [45, 46, 47, 48]. In 2003, A.
Vaziri, J. W. Pan et al. present the experimental realization of higher dimensional entangle-
ment concentration of OAM entangled photons [49]. The concentrate of hyperentangled states
considering different physical systems and DOFs has attracted much more attention rencently
[50, 51]. Here, we extensive study the concentrate way of polarization-OAM entanglement state
in different cases and discuss the implement scheme of them based on current technology.
In this paper we offer two hyperentangled concentration protocols (Hyper-ECPs) of two-
photon entanglement with OAM and polarization DOFs. The first one is concentrating one
maximally hyperentangled Bell-like state from two partial hyperentangled state with unknown
parameters. The second concentration scheme only needs one less-entangled state with known
parameters via higher efficiency. Both of the schemes can be generalized to multi-photons
hyperentangled concentration as in [51], and the efficiencies should be the highest in different
case. Our schemes can be exploited in long distance communication effectively and expediently.
1 hyperentanglement concentration scheme with
unknown parameters
Without loss of generality, we suppose the two photons in the following hyperentangled
state initially [34]
|φ
AB
=(α |HH+ β |VV)
AB
⊗ (δ |l, l + η |−l, −l)
AB
. (1)
Where |H and |V represent the horizontal state and vertical state of polarization DOF,
respectively. |l and |−l denote the states of photon with the l and −l quantum numbers of
AOM, respectively. The subscripts A and B make a distinction between the photons belongs to
Alice and Bob who have a great distance off. α, β, δ and η are normalization constant satisfied
|α|
2
+ |β|
2
= 1 and |δ|
2
+ |η|
2
= 1. In most of the QIPs, the maximally hyperentangled Bell-like
states with α = β =
1
√
2
and δ = η =
1
√
2
are used to transmit information as quantum channel.
So we wish to concentrate the following state from state (1)
|φ
AB
=
1
2
(|HH + |VV)
AB
⊗ (|l, l+ |−l, −l)
AB
. (2)
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