Alternative names: Entanglement-assisted classical communication (EACC) code, Entanglement-assisted classical code.
Root code for the Classical-quantum Domain
Codes for classical communication over quantum channels
Description
Classical-quantum code whose encoding and decoding utilize pre-shared entanglement between sender and receiver. The sender encodes classical information into quantum systems sent through a quantum channel, while the receiver decodes using the channel outputs together with retained halves of pre-shared entangled states.Protection
A finite-block EACC code is often denoted by \([n,k,d;c]_q\), where \(n\) is the number of \(q\)-dimensional channel uses, \(q^k\) is the number of classical messages, \(d\) is the minimum distance, and \(c\) is the number of pre-shared maximally entangled qudit pairs. Such a code corrects \(d-1\) erasures or \(\left\lfloor(d-1)/2\right\rfloor\) errors in the setting of Ref. [1].Rate
The entanglement-assisted classical capacity \(C^{\rm ea}(T)\) is the highest asymptotic rate for reliable classical communication through a quantum channel \(T\) when arbitrary pre-shared entanglement is available [2,3]. For lossy bosonic channels with high thermal noise and low transmitted photon number, pre-shared entanglement can yield a capacity ratio scaling as \(\log(1/N_S)\) relative to the unassisted Holevo capacity [4,5]. If the encoding and decoding circuits themselves are noisy, the fault-tolerant EA capacity approaches the usual EA capacity as the gate error tends to zero [6].Encoding
Super-dense coding maps two \(q\)-ary classical symbols to one transmitted qudit when one maximally entangled qudit pair is available [7].Cousins
- Bosonic c-q code— Bosonic EA c-q schemes use pre-shared continuous-variable entanglement to assist bosonic c-q communication, including structured transceivers for lossy thermal-noise channels [4,5].
- Entanglement-assisted (EA) hybrid QECC— EA c-q codes transmit only classical information with entanglement assistance, while EA hybrid QECCs transmit both classical and quantum information with entanglement assistance.
- Entanglement-assisted (EA) QECC— EA c-q codes transmit classical information with entanglement assistance, while EAQECCs transmit quantum information with entanglement assistance.
Primary Hierarchy
Parents
An EAOA QECC that has no gauge structure (e.g., gauge qubits), that has a block structure that corresponds to a classical code, that stores no quantum information, and that utilizes pre-shared entanglement is an EA c-q code.
Entanglement-assisted (EA) c-q code
Children
References
- [1]
- T. Prasad and M. Grassl, “Codes for entanglement-assisted classical communication”, npj Quantum Information 11, (2025) arXiv:2310.19774 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) DOI
- [3]
- C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem”, IEEE Transactions on Information Theory 48, 2637 (2002) DOI
- [4]
- S. Guha, Q. Zhuang, and B. A. Bash, “Infinite-fold enhancement in communications capacity using pre-shared entanglement”, 2020 IEEE International Symposium on Information Theory (ISIT) 1835 (2020) arXiv:2001.03934 DOI
- [5]
- A. Cox, Q. Zhuang, C. N. Gagatsos, B. Bash, and S. Guha, “Transceiver Designs Approaching the Entanglement-Assisted Communication Capacity”, Physical Review Applied 19, (2023) arXiv:2208.07979 DOI
- [6]
- P. Belzig, M. Christandl, and A. Müller-Hermes, “Fault-Tolerant Coding for Entanglement-Assisted Communication”, IEEE Transactions on Information Theory 70, 2655 (2024) arXiv:2210.02939 DOI
- [7]
- C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states”, Physical Review Letters 69, 2881 (1992) DOI
Page edit log
- Victor V. Albert (2026-05-26) — most recent
Cite as:
“Entanglement-assisted (EA) c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/ea_classical_into_quantum