We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, Dur, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution
We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, Dür, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the tradeoff in the secret key rate between the communication time and the required resources. For this purpose, we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given in [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in the encoded connection procedure of this repeater and develop a suitable decoding algorithm. Furthermore, we derive the rate of producing entangled pairs for the quantum repeater using encoding and give the minimal parameters (gate quality and initial fidelity) for establishing a nonzero secret key. We find that the generic quantum repeater is optimal regarding the secret key rate per memory per second and show that the encoded quantum repeater using the simple three-qubit repetition code can even have an advantage with respect to the resources compared to other recent quantum repeater schemes with encoding.
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10 4 − 10 5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.
We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. We finally study the effect of the detector efficiency on the secret key rate.
We develop a new method to quantify the secret key rate for permutation-invariant protocols for coherent attacks and finite resources. The method reduces the calculation of secret key rates for coherent attacks to the calculation for collective attacks by bounding the smooth min-entropy of permutation-invariant states via the smooth min-entropy of corresponding tensor-product states. The comparison of the results to the well-known post-selection technique for the BB84 and six-state protocol shows the high relevance of this method. Since our calculation of secret key rates for coherent attacks strongly depends on the way of treating collective attacks, a prospective progress in the analysis of collective attacks will immediately cause progress in our strategy.
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