Quantum circuit for security proof of quantum key distribution without encryption of error syndrome and noisy processing

TL;DR

This paper introduces a quantum circuit for the security proof of quantum key distribution that eliminates the need for encrypting the error syndrome and explains how noise addition enhances security thresholds.

Contribution

It constructs a quantum circuit for the virtual protocol, removing classical postprocessing limitations and providing an intuitive understanding of noise effects on security.

Findings

Eliminates the need for syndrome encryption in QKD security proof

Provides an intuitive proof for noise increasing the error threshold

Bridges simple security proofs with broader classical postprocessing methods

Abstract

One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted key increases the bit error rate threshold in the general case in which one of the parties does not possess a qubit. Thus, our circuit bridges the simple proof and the use of wider classes of classical postprocessing.