A Decoupling Approach to the Quantum Capacity
Open accessAbstract
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will, with high probability, be decoupled from the channel environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modification yielding unitarily invariant ensembles of maximally entangled codes.
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The decoupling approach essentially involves deriving entanglement wedge reconstruction from the Ryu-Takayanagi formula.
“Indeed, one of the most popular methods to prove results about error correction in random unitaries, the so-called decoupling approach [71, 72], essentially involves deriving entanglement wedge reconstruction from the Ryu-Takayanagi formula.”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [71]
Cites
The ‘transition probability’ in the state space of a—algebra
Uhlmann, A. (1976) · Reports on Mathematical Physics · doi:10.1016/0034-4877(76)90060-4 · Cited by 1,649 · see citing works
The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information
Devetak, I., & Shor, P. W. (2005) · Communications in Mathematical Physics · doi:10.1007/s00220-005-1317-6 · Cited by 445 · see citing works
Quantum-channel capacity of very noisy channels
DiVincenzo, D. P., Shor, P. W., & Smolin, J. A. (1998) · Physical Review A · doi:10.1103/physreva.57.830 · Cited by 297 · see citing works
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Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
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Hayden, P., & Preskill, J. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/09/120 · Cited by 1,332 · see citing works
Self-citationThe Theory of Quantum Information
Watrous, J. (2018) · doi:10.1017/9781316848142 · Cited by 1,325 · see citing works
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Entanglement wedge reconstruction and the information paradox
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Harrow, A. W., & Low, R. A. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0873-6 · Cited by 324 · see citing works
“This technique is used in [2] to construct a variety of encoding circuits for tasks in quantum Shannon theory; thus, we (like [10]) reduce the encoding complexity in [2] (and related works, such as [21]) to O ( n 2 ).”
MethodA Survey on Quantum Channel Capacities
Gyongyosi, L., Imre, S., & Nguyen, H. V. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2786748 · Cited by 337 · see citing works
Entanglement-Assisted Quantum Turbo Codes
Wilde, M. M., Hsieh, M.-H., & Babar, Z. (2014) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2292052 · Cited by 102 · see citing works
Speed limits in Liouville space for open quantum systems
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Self-citationApproximate Quantum Error Correction Revisited: Introducing the Alpha-Bit
Hayden, P., & Penington, G. (2020) · Communications in Mathematical Physics · doi:10.1007/s00220-020-03689-1 · Cited by 40 · see citing works
Self-citation
- Authors
- Hayden, P., Horodecki, M., Winter, A., & Yard, J.
- Affiliations
- McGill University (CA)
- University of Gdańsk (PL)
- University of Bristol (GB)
- California Institute of Technology (US)
- Venue
- Open Systems & Information Dynamics
- Publisher
- World Scientific Pub Co Pte Ltd
- Published
- 2008-03
- Volume
- 15
- Issue
- 01
- Pages
- 7-19
- ISSN
- 1230-1612 (ISSN-L)
- 1793-7191
- OpenAlex
- W1975313455
- Cited by
- 170
- References
- 3
- Citations by year
- 2026: 9 · 2025: 8 · 2024: 8 · 2023: 8 · 2022: 10 · 2021: 18 · 2020: 9 · 2019: 9 · 2018: 9 · 2017: 5 · 2016: 13 · 2015: 7 · 2014: 14 · 2013: 5 · 2012: 7
- FWCI
- 15.33
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Open Systems & Information Dynamics (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum channel capacity, coherent information, decoupling, noisy quantum channels
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