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arXiv:1610.04828 · Optical Engineering

Long-distance quantum key distribution using concatenated entanglement swapping with practical resources

Aeysha Khalique, Barry C. Sanders

Published Jan 25, 2017• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1117/1.oe.56.1.016114

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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.
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.
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.
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.
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​.
This paper investigates a novel approach to enhancing cryptographic key distribution using entanglement swapping. Current quantum key distribution (QKD) protocols are often limited by distance due to signal loss and decoherence during the direct transmission of entangled photons. This research proposes a protocol that overcomes these limitations by employing entanglement swapping, effectively extending the range of secure key exchange. The core of the method involves strategically swapping entangled pairs to create correlated states between distant parties, circumventing the need for direct transmission over long distances. Mathematical formulations detailing the protocol's key steps, including the quantum operations and measurement outcomes, are presented. The analysis demonstrates a pathway towards significantly increasing the practical range of QKD systems, offering a potential solution for secure communication over greater distances. The theoretical framework presented here lays the groundwork for future experimental implementations and further optimization of entanglement swapping protocols for enhanced QKD performance.