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Computer Programming Skills & Maintenance

Explain on Application of Quantum LDPC Codes in Quantum Key Distribution

Wang Xi

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

This article will BB84 key distribution protocol seen as a Wire-tap channel model, the main channel is a binary symmetric channel, bit flipping rate 0.25e, Wire-tap channel is a binary erasure channel, deleted probability 1-e, through quantum LDPC coding way, in the BB84 write about the main channel to achieve secure communication, while the security of the BB84 protocol proof. Finally, the Wire-tap channel capacity of safety is calculated, and ultimately get the BB84 protocol of quantum LDPC codes under the tolerable error rate.

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This article will BB84 key distribution protocol seen as a Wire-tap channel model, the main channel is a binary symmetric channel, bit flipping rate 0.25e, Wire-tap channel is a binary erasure channel, deleted probability 1-e, through quantum LDPC coding way, in the BB84 write about the main channel to achieve secure communication, while the security of the BB84 protocol proof. Finally, the Wire-tap channel capacity of safety is calculated, and ultimately get the BB84 protocol of quantum LDPC codes under the tolerable error rate.
In this paper,the security of BB84 key distribution protocol is considered.We assume that in the protocol the eavesdropper Eve intercepts/resends photons transmitted between Alice and Bob with probability e.First,the BB84 key distribution protocol will be made equivalent to a special Wire-tap channel model,where the main channel is a binary symmetric channel with probability of flipping bits 0.25e and the eavesdropper's channel is a binary erasure channel with probability of erasure 1-e.Using the coding method and properties of quantum LDPC codes CSS(C1,C2) for secure communication across the Wire-tap channel in the BB84 protocol is an equivalent proof of the security of BB84 protocol.Finally,the tolerable error rate of the BB84 protocol based on quantum LDPC codes can be obtained by calculating the secrecy capacity of this special Wire-tap channel.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical errorcorrecting codes for both error correction (for the honest p arties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel system introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channel systems. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel system and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.
Considering noise in the quantum channel of BB84 quantum key distribution protocol,an improved model of BB84 protocol with quantum error correction code,such as Quantum Low Density Parity Check code(QLDPC) is proposed in this paper.By numerical simulation,the effect of quantum error correction code on BB84 protocol is analyzed in the case of the efficiency of transmission rate.The results show that quantum LDPC codes have good ability to overcome the noise,raise the efficiency of transmission rate and verify the availability of the improved model.
Quantum encryption guarantees the absolute security of key distribution from the physical mechanism. However, in the process of quantum key distribution (QKD), quantum channel noise will reduce the transmission efficiency. Quantum low-density parity check (quantum LDPC) code has become a hot research topic of quantum error correcting code due to its great flexibility in the choice of code length and code rate and its dependence on sparse graphs. In order to improve the transmission reliability, a QKD protocol based on BB84 and quantum LDPC code is designed. First, we construct a quantum LDCP error correcting code. Then we utilize the error correcting code and BB84 to construct our QKD protocol. Finally, we analyze the influence of the quantum LDPC code on the proposed protocol. The results show that the key transmission efficiency of the our protocol is improved, and the validity of the QKD protocol based on BB84 and quantum LDPC codes in noisy quantum channels is verified.
Quantum key distribution (QKD) enables secure communication using the principles of quantum physics. The BB84 protocol is not only effective for secure key sharing but also for detecting eavesdropping. This study simulates a computational model of QKD and analyzes error rates under varying numbers of bits. Using Python-based simulations with n = 10, n = 100, and n = 1000 bits, and a fixed noise probability of 0.02, we evaluated scenarios both with and without eavesdropping over 1000 trials. The results show an average error rate of 2% without eavesdropping and over 26% with eavesdropping. Standard deviation increases with lower n, indicating higher variability. This study validates BB84’s robustness under noise and demonstrates its sensitivity to third-party interference.