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arXiv:0904.1184 · Physical Review A

Quantum states prepared by realistic entanglement swapping

Artur Scherer, Regina B. Howard, Barry C. Sanders, Wolfgang Tittel

Published Dec 4, 2009• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.80.062310

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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.
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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.
Abstract The aim of this paper is to swap the entanglement between two separate long-distant locations. The well-known entangled coherent states as two-mode continuous-variable states are very interesting in quantum teleportation and entanglement swapping processes. To make our investigation more realistic, by using such entangled states as the building blocks of our quantum repeater protocol, the effect of decoherence on the swapped entanglement is also considered. We explicitly establish our model for four locations; moreover, we find that our model can be extended to 2 N locations, where . Consequently, we can introduce this model as a quantum repeater, which is helpful for entanglement swapping to long-enough distances.