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EA qubit code

Root code for the Qubit Kingdom

Description

Qubit code designed to utilize pre-shared entanglement between sender and receiver.

Protection

The quantum GV bound and Plotkin bound have been extended to EA qubit codes [1].

Rate

There are EA versions of classical and quantum capacities [2], and the ratio of the entanglement-assisted and unassisted classical capacities of a channel is bounded by a function of the input channel's dimension [3]. EA hashing bounds on the minimum entanglement required to achieve the entanglement-assisted channel capacity are derived [4].

Encoding

Encoding algorithm [5].

Decoding

Decoding algorithm [5].

Cousins

  • Qubit code— EA qubit codes utilize additional ancillary qubits in a pre-shared entangled state, but reduce to ordinary qubit codes when said qubits are interpreted as noiseless physical qubits.
  • Codeword stabilized (CWS) code— EA CWS codes have been formulated [6].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Parents
EA Galois-qudit codeEAQECC Quantum
EA Galois-qudit codes reduce to EA qubit codes for \(q=2\).
EA qubit code
Children
EA qubit stabilizer code

References

[1]
C.-Y. Lai, T. A. Brun, and M. M. Wilde, “Dualities and identities for entanglement-assisted quantum codes”, Quantum Information Processing 13, 957 (2013) arXiv:1010.5506 DOI
[2]
C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-Assisted Classical Capacity of Noisy Quantum Channels”, Physical Review Letters 83, 3081 (1999) arXiv:quant-ph/9904023 DOI
[3]
L. H. Wolff, P. Belzig, M. Christandl, B. Durhuus, and M. Tomamichel, “Fundamental Limit on the Power of Entanglement Assistance in Quantum Communication”, Physical Review Letters 134, (2025) arXiv:2408.17290 DOI
[4]
G. Bowen, “Entanglement required in achieving entanglement-assisted channel capacities”, Physical Review A 66, (2002) arXiv:quant-ph/0205117 DOI
[5]
M. M. Wilde, “Quantum Coding with Entanglement”, (2008) arXiv:0806.4214
[6]
J. Shin, J. Heo, and T. A. Brun, “Entanglement-assisted codeword stabilized quantum codes”, Physical Review A 84, (2011) arXiv:1109.3358 DOI
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Zoo Code ID: ea_qubits_into_qubits

Cite as:
“EA qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ea_qubits_into_qubits
BibTeX:
@incollection{eczoo_ea_qubits_into_qubits, title={EA qubit code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ea_qubits_into_qubits} }
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Permanent link:
https://errorcorrectionzoo.org/c/ea_qubits_into_qubits

Cite as:

“EA qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ea_qubits_into_qubits

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/ea_qubits_into_qubits.yml.