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Paper 1
An Efficient Error Estimation Method in Quantum Key Distribution
Yingjian Wang, Yilun Hai, Buniechukwu Njoku, Koteswararao Kondepu, Riccardo Bassoli, Frank H. P. Fitzek
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2411.07160
- arXiv
- 2411.07160
Error estimation is an important step for error correction in quantum key distribution. Traditional error estimation methods require sacrificing a part of the sifted key, forcing a trade-off between the accuracy of error estimation and the size of the partial sifted key to be used and discarded. In this paper, we propose a hybrid approach that aims to preserve the entire sifted key after error estimation while preventing Eve from gaining any advantage. The entire sifted key, modified and extended by our proposed method, is sent for error estimation in a public channel. Although accessible to an eavesdropper, the modified and extended sifted key ensures that the number of attempts to crack it remains the same as when no information is leaked. The entire sifted key is preserved for subsequent procedures, indicating the efficient utilization of quantum resources.
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Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound
Soham Ghosh, Evagoras Stylianou, Holger Boche
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04130
- arXiv
- 2410.04130
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3} $. For higher rates, our EAQECC also meets the Singleton bound, although with increased entanglement requirements. Additionally, we demonstrate that any classical $[n,k,d]_q$ code can be transformed into an EAQECC with parameters $[[n,k,d;2k]]_q$ using $2k$ pre-shared maximally entangled pairs. The complexity of our encoding protocol for $k$-qudits with $q$ levels is $\mathcal{O}(k \log_{\frac{q}{q-1}}(k))$, excluding the complexity of encoding and decoding the classical MDS code. While this complexity remains linear in $k$ for systems of reasonable size, it increases significantly for larger-levelled systems, highlighting the need for further research into complexity reduction.
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