Quantum-channel capacity of very noisy channels
Open accessAbstract
We present a family of additive quantum error-correcting codes whose capacities exceed those of quantum random coding (hashing) for very noisy channels. These codes provide nonzero capacity in a depolarizing channel for fidelity parameters $f$ when $f>0.80944$. Random coding has nonzero capacity only for $f>0.81071$; by analogy to the classical Shannon coding limit, this value had previously been conjectured to be a lower bound. We use the method introduced by Shor and Smolin of concatenating a nonrandom repetition (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal for single concatenation. The best known multiple-concatenated code we found has a block size of 25. We derive a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states.
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If unbiased one-qubit EPGs exceed 0.5, then the effect of gates can be simulated classically.
“It is known that if unbiased one-qubit EPGs exceed . 5 , then we can simulate the effect of gates classically. 31, 32”
From Quantum computing with realistically noisy devices (2005) · cites this paper as [32]
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Brádler, K., Dutil, N., Hayden, P. M., & Muhammad, A. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3449555 · Cited by 48 · see citing works
Additive extensions of a quantum channel
Smith, G., & Smolin, J. A. (2008) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw.2008.4578688 · Cited by 47 · see citing works
Self-citationSemidefinite Programming Converse Bounds for Quantum Communication
Wang, X., Fang, K., & Duan, R. (2019) · UTS ePRESS (University of Technology Sydney) · Cited by 46 · see citing works
Quantum and Private Capacities of Low-Noise Channels
Leditzky, F., Leung, D., & Smith, G. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.160503 · Cited by 46 · see citing works
The quantum capacity with symmetric side channelsPreprint
Smith, G., Smolin, J. A., & Winter, A. (2006) · Cited by 46 · see citing works
Self-citationBias-tailored quantum LDPC codes
Roffe, J., Cohen, L. Z., Quintavalle, A. O., Chandra, D., & Campbell, E. T. (2023) · Quantum · doi:10.22331/q-2023-05-15-1005 · Cited by 44 · see citing works
Semidefinite Programming Converse Bounds for Quantum Communication
Wang, X., Fang, K., & Duan, R. (2018) · IEEE Transactions on Information Theory · doi:10.1109/tit.2018.2874031 · Cited by 44 · see citing works
“Pretty Strong” Converse for the Quantum Capacity of Degradable Channels
Morgan, C., & Winter, A. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2288971 · Cited by 43 · see citing works
Noisy Processing and Distillation of Private Quantum States
Renes, J. M., & Smith, G. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.020502 · Cited by 43 · see citing works
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Babar, Z., Botsinis, P., Alanis, D., Ng, S. X., & Hanzo, L. (2015) · IEEE Access · doi:10.1109/access.2015.2405533 · Cited by 40 · see citing works
Superadditivity of Private Information for Any Number of Uses of the Channel
Elkouss, D., & Strelchuk, S. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.040501 · Cited by 39 · see citing works
Quantum Flags and New Bounds on the Quantum Capacity of the Depolarizing Channel
Fanizza, M., Kianvash, F., & Giovannetti, V. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.020503 · Cited by 38 · see citing works
Quantum codes from neural networks
Bausch, J., & Leditzky, F. (2019) · Apollo (University of Cambridge) · doi:10.17863/cam.48816 · Cited by 45 · see citing works
Enhanced estimation of a noisy quantum channel using entanglement
Fischer, D. G., Mack, H., Cirone, M. A., & Freyberger, M. (2001) · Physical Review A · doi:10.1103/physreva.64.022309 · Cited by 38 · see citing works
Capacities of Quantum Channels and How to Find ThemPreprint
Shor, P. W. (2003) · Cited by 43 · see citing works
Self-citationPotential Capacities of Quantum Channels
Winter, A., & Yang, D. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2519920 · Cited by 37 · see citing works
- Authors
- DiVincenzo, D. P., Shor, P. W., & Smolin, J. A.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- AT&T (United States) (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1998-02-01
- Volume
- 57
- Issue
- 2
- Pages
- 830-839
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1970302872
- Cited by
- 297
- References
- 26
- Citations by year
- 2026: 7 · 2025: 12 · 2024: 10 · 2023: 10 · 2022: 17 · 2021: 17 · 2020: 13 · 2019: 7 · 2018: 18 · 2017: 10 · 2016: 9 · 2015: 9 · 2014: 13 · 2013: 11 · 2012: 12
- FWCI
- 10.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- quantum channel capacity, depolarizing channel, random coding, hashing, cat codes, concatenated codes, coherent information
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