Master´s Thesis Defense by Eva González Ruiz

Study of InGaAs quantum dots as single-photon sources for Device-Independent Quantum Key Distribution

A loophole-free violation of Bell’s inequality is required for Device-Independent Quantum Key Distribution (DIQKD) protocols to work, requiring a certain efficiency of the source. Both the locality and detection loopholes must be closed; however, while closing the locality loophole only requires ensuring a determined distance between Alice and Bob, the detection loophole demands very high transmission efficiencies [1]. To overcome it, we have introduced a heralding scheme proposed by [2] that, furthermore, creates entanglement by measurement between the pair of photons shared by Alice and Bob, thus avoiding the potential action of the eavesdropper on the state. We have studied the reliability of InGaAs quantum dots as single-photon sources for the completion of the protocol, with the intention of implementing DIQKD based on them in the near future. We have analyzed both the influence of distinguishability and losses, together with the limitations in the resolution of the number of photons in the detection. We have studied the effect of the distinguishability of photons by relating it to the HOM visibility of the sources, finding a threshold of V ≈ 79%. This visibility is accomplishable by InGaAs quantum-dot single-photon sources [3]. However, the relation obtained between the local efficiency and the required visibility shows that the necessary local efficiencies (ηl ≈ 90%) are yet not achievable with current photonic implementations [4]. Finally, we have aimed to find the best compromise between a high heralding rate and the probability of receiving incorrect messages of success from the heralding station by optimizing the probability of transmission T of the local beam splitters. We find that the optimal probability of transmission decreases with the distinguishability of photons. Our results show that the necessary experimental time to accomplish the violation of Bell’s inequality with several standard deviations is not unreasonable.

[1]  Stefano Pironio, Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani. Device-independent quantum key distribution secure against collective attacks. New Journal of Physics, 11(4):045021, apr 2009.
[2]  Alejandro Máttar, Jan Kołodyński, Paul Skrzypczyk, Daniel Cavalcanti, Konrad Banaszek, and Antonio Acín. Device-independent quantum key distribution with single-photon sources.arXiv e-prints, page arXiv:1803.07089, Mar 2018.
[3]  Gabija Kiršanske ̇, Henri Thyrrestrup, Raphaël S. Daveau, Chris L. Dreeßen, Tommaso Pregnolato, Leonardo Midolo, Petru Tighineanu, Alisa Javadi, Søren Stobbe, Rüdiger Schott, Arne Ludwig, Andreas D. Wieck, Suk In Park, Jin D. Song, Andreas V. Kuhlmann, Immo Söllner, Matthias C. Löbl, Richard J. Warburton, and Peter Lodahl. Indistinguishable and efficient single photons from a quantum dot in a planar nanobeam waveguide. Phys. Rev. B, 96:165306, Oct 2017.
[4]  Thomas Hummel, Claudéric Ouellet-Plamondon, Ela Ugur, Irina Kulkova, Toke Lund-Hansen, Matthew A. Broome, Ravitej Uppu, and Peter Lodahl. Efficient demultiplexed single-photon source with a quantum dot coupled to a nanophotonic waveguide. Applied Physics Letters, 115(2):021102, 2019.