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Journal of Optics

The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum

Sandeep K. Goyal, Alpha Hamadou Ibrahim, Filippus Stefanus Roux, Thomas Konrad, Andrew Forbes

Published Apr 5, 2016• 34 citations
Publisher

Abstract

Abstract Using an experimental setup that simulates a turbulent atmosphere, we study the secret key rate for quantum key distribution (QKD) protocols in orbital angular momentum based free space quantum communication. The QKD protocols under consideration include the Ekert 91 protocol for different choices of mutually unbiased bases and the six-state protocol. We find that the secret key rate of these protocols decay to zero, roughly at the same scale where the entanglement of formation decays to zero.

DOI
10.1088/2040-8978/18/6/064002

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Abstract Using an experimental setup that simulates a turbulent atmosphere, we study the secret key rate for quantum key distribution (QKD) protocols in orbital angular momentum based free space quantum communication. The QKD protocols under consideration include the Ekert 91 protocol for different choices of mutually unbiased bases and the six-state protocol. We find that the secret key rate of these protocols decay to zero, roughly at the same scale where the entanglement of formation decays to zero.
Using an experimental setup that simulates a turbulent atmosphere, we study the secret key rate for quantum key distribution protocols in orbital angular momentum based free space quantum communication. The quantum key distribution protocols under consideration include the Ekert 91 protocol for different choices of mutually unbiased bases and the six-state protocol. We find that the secret key rate of these protocols decay to zero roughly at the same scale where the entanglement of formation decays to zero.
In this paper, a free-space quantum key distribution (QKD) system based on BB84 protocol is studied assuming that the transmitted quantum bits are multiplexed spatially based on orthogonal orbital angular momentum (OAM) carrying beams. The performance of such a system is estimated in terms of quantum bit error rate, outage capacity, and effective data rate taking into account the impact of error correction and privacy amplification. Based on the simulation of OAM-carrying beam propagating through atmospheric channels impaired by turbulence, the crosstalk among the multiplexed channels are investigated and its effect on the performance of the QKD system is evaluated. The presented results provide insight into the efficient design of such multiplexed QKD systems particularly in terms of the choice of the optimal average photon number per pulse and the multiplexing mode set.
Quantum key distribution (QKD) technology has demonstrated remarkable practicality and sustained developmental trends in the current field of quantum communication. This paper focuses on a novel and potent quantum communication protocol, specifically quantum key distribution utilizing the encoding of information through orbital angular momentum (OAM) of photons. OAM states, owing to their distinctive properties, exhibit significant advantages in terms of information capacity and channel robustness. However, the sensitivity of OAM states to atmospheric conditions and challenges arising from wavefront distortions necessitate in-depth investigation. Additionally, the unique structure of OAM beams has raised concerns about geometric losses. By analyzing the impact of atmospheric turbulence and geometric losses on the transmission performance when applying the OAM-QKD protocol in free space, this paper explores variations in system losses under different OAM orders. Simulation results indicated that as the channel distance increases, system losses gradually escalate. Furthermore, with an increase in OAM order, although the system's sensitivity to atmospheric turbulence diminishes, geometric losses exhibit an exponential increase. Addressing this issue, our research suggested that when considering free-space quantum key distribution with OAM encoding, selecting an OAM order of 1 for the beam achieves minimal transmission losses. Therefore, in practical applications, employing OAM beams with <?TeX l=1l = 1l=1 ?> emerges as an effective strategy to optimize the performance of the OAM-QKD protocol in free space.
The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement-based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects measurements during periods of low transmission efficiency, where the measured quantum bit error rate is temporarily elevated. Using this, we increase the total secret key generated by the system from 78 009 bits to 97 678 bits, representing an increase of 25.2% in the final secure key rate, generated from the same raw signals. Lastly, we present simulations of a QKD exchange with an orbiting low earth orbit satellite and show that an SNRF will be extremely useful in such a situation, allowing many more passes to extract a secret key than would otherwise be possible.
We study the evolution of an orbital angular momentum (OAM) entangled bipartite photonic state for the case where one of the photons propagates through Kolmogorov turbulence, using the concurrence as a measure of entanglement. Quantum state tomography was performed to reconstruct the two qubit density matrices for a range of scintillation strengths. Our results give the first direct experimental confirmation of the existing theories for decay of entanglement due to atmospheric turbulence. We also show how the modal scattering increases with increasing scintillation and we discuss the impact of the scale at which entanglement dissipates due to atmospheric turbulence on free-space quantum communication.