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arXiv:1407.1568 · Physical Review A

Long-distance quantum communication through any number of entanglement-swapping operations

Aeysha Khalique, Barry C. Sanders

Published Sep 3, 2014• 26 citations
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Abstract

We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement-swapping operations and solve numerically for up to three intermediate entanglement-swapping operations. Our model yields two-photon interference visibilities postselected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through the parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.

DOI
10.1103/physreva.90.032304

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We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement-swapping operations and solve numerically for up to three intermediate entanglement-swapping operations. Our model yields two-photon interference visibilities postselected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through the parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.
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We develop a model for practical, entanglement-based long-distance quantum key distribution employing entanglement swapping as a key building block. Relying only on existing off-the-shelf technology, we show how to optimize resources so as to maximize secret key distribution rates. The tools comprise lossy transmission links, such as telecom optical fibers or free space, parametric down-conversion sources of entangled photon pairs, and threshold detectors that are inefficient and have dark counts. Our analysis provides the optimal trade-off between detector efficiency and dark counts, which are usually competing, as well as the optimal source brightness that maximizes the secret key rate for specified distances (i.e. loss) between sender and receiver.
In this dissertation I develop a Monte-Carlo sampling approach to redress the enormous computational time required to calculate two-photon visibility for multiple-entanglementswapping-based long-distance quantum communication. I employ our theory to study both the realistic setting involving dark counts, multi-photon events and loss, and I also study the semi-idealistic case of perfect synchronized single-photon sources; this semi-idealistic case is used to verify my sampling method. My new sampling method enables successful, reliable calculation of visibility for up to six consecutive entanglementswapping stations. Although six entanglement-swapping stations lead to extremely low rates in the real-world setting, my sampling method for solving long-distance quantum communication rates and visibility serves as a valuable tool for modeling future viable quantum communication strategies incorporating promising technology such as optical quantum memory. past twenty-three years, and my dear friends, without whom my life can never be that wonderful. Finally, I want to thank her, who is the reason why I never give up on this project.
We present our approach for sharing photons and assessing resultant four-photon visibility between two distant parties using concatenated entanglement swapping. In addition we determine the corresponding key generation rate and the quantum bit-error rate. Our model is based on practical limitations of resources, including multipair parametric down-conversion sources, inefficient detectors with dark counts and lossy channels. Through this approach, we have found that a trade-off is needed between experimental run-time, pair-production rate and detector efficiency. Concatenated entanglement swapping enables huge distances for quantum key-distribution but at the expense of low key generation rate.
We develop a theory for long-distance quantum key distribution based on concatenated entanglement swapping using parametric down-conversion sources and show the numerical results of our model. The model incorporates practical resources including multipair sources, inefficient detectors with dark counts, and lossy channels. We calculate the maximum secret key-generation rate for up to three entanglement swapping stations by optimizing resource parameters. Our numerical simulation shows that the range of quantum key distribution can, in principle, be markedly increased but at the expense of an atrociously unfeasible secret key-generation rate; however, the upper bound of our key rates closely approaches the Takeoka–Guha–Wilde upper bound. Our analysis demonstrates the need for new technology, such as quantum memory, to synchronize photons; our methods should serve as a valuable component for accurately modeling quantum-memory-based long-distance quantum key distribution.
Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays or quantum repeaters to overcome the range limits of long-distance quantum key distribution. We develop a closed-form solution for the actual quantum states prepared by realistic entanglement swapping, which takes into account experimental deficiencies due to inefficient detectors, detector dark counts, and multiphoton-pair contributions of parametric down-conversion sources. We investigate how the entanglement present in the final state of the remaining modes is affected by the real-world imperfections. To test the predictions of our theory, comparison with previously published experimental entanglement swapping is provided.