Access the full text.
Sign up today, get DeepDyve free for 14 days.
T Brun, I Devetak, MH Hsieh (2006)
Correcting quantum errors with entanglementScience, 314
CY Lai, TA Brun, MM Wilde (2013)
Duality in entanglement-assisted quantum error correctionIEEE Trans. Inf. Theory, 59
AR Calderbank, EM Rains, PW Shor, NJA Sloane (1998)
Quantum error-correction via codes over GF(4)IEEE. Trans. Inf. Theory, 44
CH Bennett, PW Shor, JA Smolin, AV Thapliyal (1999)
Entanglement-assisted classical capacity of noisy quantum channelsPhys. Rev. Lett., 83
I Bouyukliev, M Grassl, Z Varbanov (2004)
New bounds for $$n_{4}$$ n 4 (k, d) and classification of some optimal codes over GF(4)Discret. Math., 281
I Devetak, AW Harrow, A Winter (2008)
A resource framework for quantum Shannon theoryIEEE Trans. Inf. Theory, 54
TA Brun, I Devetak, MH Hsieh (2014)
Catalytic quantum error correctionIEEE Trans. Inf. Theory, 60
MM Wilde, TA Brun (2008)
Optimal entanglement formulas for entanglement-assisted quantum codingPhys. Rev. A, 77
PP Greenough, R Hill (1994)
Optimal linear codes over GF(4)Discret. Math., 125
D Gottesman (1996)
Class of quantum error-correcting codes saturating the quantum Hamming boundPhys. Rev. A, 54
G Bowen (2002)
Entanglement required in achieving entanglement-assisted channel capacitiesPhys. Rev. A, 66
CY Lai, TA Brun (2012)
Entanglement-assisted quantum error correcting codes with imperfect ebitsPhys. Rev. A, 86
Z Wan (1993)
Geometry of Classical Groups over Finite Fields
MM Wilde, MH Hsieh, Z Babar (2014)
Entanglement-assisted quantum turbo codesIEEE Trans. Inf. Theory, 60
FR Kschischang, S Pasupathy (1992)
Some ternary and quaternary codes and associated sphere packingsIEEE Trans. Inf. Theory, 28
L Guo, R Li (2013)
Linear Plotkin bound for entanglement-assisted quantum codesPhys. Rev. A, 87
WC Huffman, V Pless (2003)
Fundamentals of Error-Correcting Codes
I Devetak, AW Harrow, A Winter (2004)
A family of quantum protocolsPhys. Rev. Lett., 93
Y Fujiwara (2013)
Quantum error correction via less noisy qubitsPhys. Rev. Lett., 110
An entanglement-assisted quantum error-correcting code (EAQECC) is a generalization of standard stabilizer quantum code. Maximal entanglement EAQECCs can achieve the EA-hashing bound asymptotically. In this work, the construction of quaternary zero radical codes is discussed, including the construction of low- dimensional quaternary codes for all code lengths and higher- dimensional quaternary codes for short lengths. Using the obtained quaternary codes, we construct many maximal entanglement EAQECCs with very good parameters. Some of these EAQECCs are optimal codes, and some of them are better than previously known ones. Combining these results with known bounds, we formulate a table of upper and lower bounds on the minimum distance of any maximal entanglement EAQECCs with length up to 20 channel qubits.
Quantum Information Processing – Springer Journals
Published: Sep 26, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.