Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917801753575424 |
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| author | Ghosh, Soham Stylianou, Evagoras Boche, Holger |
| author_facet | Ghosh, Soham Stylianou, Evagoras Boche, Holger |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound Ghosh, Soham Stylianou, Evagoras Boche, Holger Quantum Physics 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. |
| title | Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.04130 |