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arXiv:1012.5675 · Optics Express

Long-distance practical quantum key distribution by entanglement swapping

Artur Scherer, Barry C. Sanders, Wolfgang Tittel

Published Feb 1, 2011• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/oe.19.003004

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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.
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.
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 explain how to share photons between two distant parties using concatenated entanglement swapping and assess performance according to the two-photon visibility as the figure of merit. From this analysis, we readily see the key generation rate and the quantum bit error rate as figures of merit for this scheme applied to quantum key distribution (QKD). Our model accounts for practical limitations, including higher-order photon pair events, dark counts, detector inefficiency, and photon losses. Our analysis shows that compromises are needed among the runtimes for the experiment, the rate of producing photon pairs, and the choice of detector efficiency. From our quantitative results, we observe that concatenated entanglement swapping enables secure QKD over long distances but at key generation rates that are far too low to be useful for large separations. We find that the key generation rates are close to both the Takeoka–Guha–Wilde and the Pirandola–Laurenza–Ottaviani–Banchi bounds.
Quantum Key distribution (QKD) enables two parties, Alice and Bob, to share a sequence of random bit whose secrecy is guaranteed by the fondations of quantum physics. The natural counterpart of this genuine inviolability lies in moderate key generation rates and achievable distances, due to severe exper- imental constraints, such as photon generation probabilities, detector's inefficiencies, detector's dark counts, and losses in fiber distribution channels. As well as improving these exper- imental resources since the last couple of years, several strate- gies are developed for increasing this bit rate. One promising way consists in exploiting the spectral correlations of time- energy entangled photons, enabling higher information con- tent per paired photon. Our idea is to combine the maturity of QKD schemes with high performance standard telecom com- ponents to propose a practical scheme allowing the distribu- tion of secret bits over 200 km at unprecedented rates.
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.
We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of NNN elementary swapping segments of length L=NlL=NlL=Nl where lll is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting, and postselection, and we include effects due to multiphoton sources, transmission loss, and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range-entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case N=2N=2N=2 exactly for the ideal case (zero dark counts, unit-efficiency detectors, and no transmission loss) and numerically for N=2N=2N=2 in the nonideal case with truncation at nmax=3{n}_{\mathrm{max}}=3nmax​=3 photons in each mode. For the general case, we show that the computational complexity for the numerical solution is nmax12N{n}_{\mathrm{max}}^{12N}nmax12N​.