## The evolution of orbital-angular-momentum entanglement of photons in turbulent air.

##### Abstract

Quantum entanglement plays an important role in the emerging quantum information
processing and communications tasks. To this day, almost all these tasks use quantum
systems described by a two dimensional Hilbert space (qubits). The use of multidi-
mensionally entangled quantum systems, provides many advantages. For instance, it
has been shown that multidimensional entangled systems provide a higher information
capacity and an increased security in quantum cryptography. One way to implement
higher dimensional quantum systems is to use the orbital angular momentum (OAM)
states of light. The OAM state of light can be used to encode quantum information
onto a laser beam which can then be transmitted to a receiver through a turbulent at-
mosphere. The main question here is how does atmospheric turbulence in
uence the
encoded quantum information?
In the work that follows, we investigate theoretically and experimentally the evolu-
tion of the OAM entanglement in atmospheric turbulence. We show how atmospheric
turbulence induces cross-talk between the different OAM modes.
We rst study numerically and experimentally the decay of OAM entanglement be-
tween two qubits propagating in atmospheric turbulence. The turbulence is modelled
by a single phase screen based on the Kolmogorov theory of turbulence. It is found that
higher order modes are more robust in turbulence. We derive an empirical formula for
the distance scale at which entanglement decays in terms of the scale parameters and
the OAM value.
Then we study numerically the evolution of OAM entanglement in a turbulent atmo-
sphere modelled by a series of consecutive phase screens. It is found that the evolution
of the OAM entanglement can not always be described by a single dimensionless quan-
tity. Under certain conditions, two dimensionless parameters are required to describe
the evolution of OAM entanglement in turbulence.
The evolution of OAM entnaglement between two qutrits propagating in turbulence
is also considered, it is found that the OAM entanglement between qutrits decays at an
equal or faster rate compared to OAM entanglement between qubits.
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