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Europhysics Letters (EPL)

Protecting the orbital angular momentum of photonic qubits using quantum error correction

Kuntuo Zhu, Liuguo Yin, Chuan Xi Wang, Guilu Long

Published Dec 1, 2020• 5 citations
Publisher

Abstract

Abstract Photons with orbital angular momentum provide an infinite-dimensional Hilbert space. Here, we study the propagation of such photons in atmospheric turbulence and obtain the Kraus operator representation for the decoherence-induced noise. We apply quantum error correction to suppress this decoherence. Specifically, we treat correction as an optimization problem in which the distance between the actual channel and the desired channel is minimized. This method provides significant channel fidelity enhancement irrespective of the turbulence strength.

DOI
10.1209/0295-5075/132/50005

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Abstract Photons with orbital angular momentum provide an infinite-dimensional Hilbert space. Here, we study the propagation of such photons in atmospheric turbulence and obtain the Kraus operator representation for the decoherence-induced noise. We apply quantum error correction to suppress this decoherence. Specifically, we treat correction as an optimization problem in which the distance between the actual channel and the desired channel is minimized. This method provides significant channel fidelity enhancement irrespective of the turbulence strength.
One of the most important properties of orbital angular momentum (OAM) of photons is that the Hilbert space required to describe a general quantum state is infinite dimensional. In principle, this could allow for encoding arbitrarily large amounts of quantum information per photon, but in practice, this potential is limited by decoherence and errors. To determine whether photons with OAM are suitable for quantum communication, we numerically simulated their passage through a turbulent atmosphere and the resulting errors. We also proposed an encoding scheme to protect the photons from these errors, and characterized its effectiveness by the channel fidelity.
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. Understanding the noise processes that affect photons is essential if we desire to protect them. In this paper we use the infinitesimal propagation equation of Roux to derive a discrete Lindblad equation, and numerically study the form of the most relevant Lindblad operators. We find that the dominant Lindblad operators are those that shift the angular momentum by one unit. We explore possible schemes to protect quantum information across multiple photons by concatenating a standard quantum error-correcting code with an error-detecting code for orbital angular momentum.
Orbital angular momentum modes are a common choice for higher-dimensional encoding of photonic qubits. When transported across large distances, these qubits (or qudits) will pass through atmospheric turbulence and suffer aberrations leading to qubit errors, information loss, entanglement degradation, and loss of quantum behavior. In order to quantify some of these effects, we have developed an atmospheric turbulence emulator which allows us to finely control parameters that determine turbulence strength. In this paper, we describe our turbulence emulator and our methods of coupling orbital angular momentum qubits into the system. We present a quantitative demonstration of the degradation of classical orbital angular momentum modes in turbulence. Finally, we discuss ongoing efforts to measure the loss of quantum behavior in orbital angular momentum qubits due to atmospheric turbulence and the use of adaptive optics to mitigate some of the negative effects of atmospheric turbulence.
Inspired by recent demonstrations of orbital angular momentum-(OAM)-based single-photon communications, we propose two quantum-channel models: (i) the multidimensional quantum-key distribution model and (ii) the quantum teleportation model. Both models employ operator-sum representation for Kraus operators derived from OAM eigenkets transition probabilities. These models are highly important for future development of quantum-error correction schemes to extend the transmission distance and improve date rates of OAM quantum communications. By using these models, we calculate corresponding quantum-channel capacities in the presence of atmospheric turbulence.
The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). Due to the greater flexibility in applications and the lower loss, QAM QKD over the free-space channel is still significant. However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel under some conditions. The cross-talk induced by turbulence and the performance of AO systems are investigated in a lab-scale link with controllable turbulence. The relations between the crosstalk and AO specifications is also studied. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing and accurate wavefront correction is necessary to adequately correct turbulence-induced error.
The orbital angular momentum (OAM) state of light can potentially be used to implement higher dimensional entangled systems for quantum communication. Unfortunately, optical fibers in use today support only modes with zero OAM values. Free-space quantum communication is an alternative to traditional way of communicating through optical fibers. However the refractive index fluctuation of the atmosphere gives rise to random phase aberrations on a propagating optical beam. To transmit quantum information successfully through a free-space optical channel, one needs to understand how atmospheric turbulence influences quantum entanglement. Here, we present a numerical study of the evolution of quantum entanglement between a pair of qubits. The qubits consist of photons entangled in the OAM basis. The photons propagate in a turbulent atmosphere modeled by a series of consecutive phase screens based on the Kolmogorov theory of turbulence. Maximally entangled initial states are considered, and the concurrence is used as a measure of entanglement. We show how the evolution of entanglement is influenced by various parameters such as the beam waist, the strength of the turbulence and the wavelength of the beam. We restricted our analysis to the OAM values l = ±1 and we compared our results to previous work.