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Laser Physics Letters

Quantum key distribution through untrusted nodes: exact solution for single-photon states

S. N. Molotkov, I. V. Sinil’shchikov

Published Sep 10, 2019• 3 citations
Publisher

Abstract

Abstract A proof of the secrecy of the quantum key distribution through an untrusted node is given. The use of entropy uncertainty relations allows us to obtain an exact solution for the length of the secret key in the single-photon case. Comparison with the exact solution for the BB84 protocol is made and the principal difference in the logical structure of the key secrecy proofs in these protocols is clearly shown, which, in our opinion, is important for the development of quantum cryptography systems.

DOI
10.1088/1612-202x/ab3802

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Abstract A proof of the secrecy of the quantum key distribution through an untrusted node is given. The use of entropy uncertainty relations allows us to obtain an exact solution for the length of the secret key in the single-photon case. Comparison with the exact solution for the BB84 protocol is made and the principal difference in the logical structure of the key secrecy proofs in these protocols is clearly shown, which, in our opinion, is important for the development of quantum cryptography systems.
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One of the challenges in practical quantum key distribution is dealing with efficiency mismatch between different threshold single-photon detectors. There are known bounds for the secret key rate for the BB84 protocol with detection-efficiency mismatch provided that the eavesdropper sends no more than one photon to the legitimate receiver. Here we improve these bounds and give tight bounds for the secret key rate with a constant detection-efficiency mismatch under the same single-photon assumption. We propose a method based on the analytical minimization of the relative entropy of coherence, which can be used in other problems in quantum key distribution. Also we propose an adaptation of the decoy state method to prove the security in the case of weak coherent pulses on the source side.