Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit
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The universal subsystem recovery channel first considered in [239] reproduces the desired behavior.
“The quantum error correcting protocol which reproduces the above desired behavior is the universal subsystem recovery channel first considered in [239].”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [239]
Using the results of [62], it is possible to put strict lower bounds on the size of the non-perturbative error that must exist to avoid a cloning paradox.
“Using the results of [62], it is possible to put strict lower bounds on the size of the non-perturbative error that must exist to avoid a cloning paradox.”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
The cloning paradox can only be resolved if there is an error term in (3.9) with size at least exp(-O(δ S_BH)) [62].
“The cloning paradox can only be resolved if there is an error term in (3.9) with size at least exp(-O(δ S BH )) [62].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
As shown in [62, 67], this would imply that there must also exist a state-independent reconstruction O_code^CFT that works for the entire code space and acts only on the CFT.
“However, as shown in [62, 67], this would imply that there must also exist a stateindependent reconstruction O code CFT that works for the entire code space and acts only on the CFT.”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
It is a general fact about quantum error correction that if exact state-dependent reconstruction of operators is possible for all states in a finite-dimensional code space, then exact state-independent reconstruction is also possible for that code space [38, 62].
“It is a general fact about quantum error correction that, if exact state-dependent reconstruction of operators is possible all states in a finite-dimensional code space, then exact state-independent reconstruction is also possible for that code space [38, 62].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
Up to the unstated linear coefficient, the additional wait time agrees with random unitary toy models.
“Up to the (unstated) linear coefficient, this agrees, yet again, with random unitary toy models [8, 62].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
Exact universal subspace quantum error correction implies full quantum error correction.
“In the Schrödinger picture, which is usually used to describe quantum error correction, this corresponds to the fact that exact universal subspace quantum error correction implies full quantum error correction[62].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [62]
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Self-citation
- Authors
- Hayden, P., & Penington, G.
- Affiliations
- Stanford University (US)
- Venue
- Communications in Mathematical Physics
- Published
- 2020-02-10
- Volume
- 374
- Issue
- 2
- Pages
- 369-432
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2729893749
- Cited by
- 40
- References
- 52
- Citations by year
- 2025: 5 · 2024: 9 · 2023: 7 · 2022: 6 · 2021: 5 · 2020: 4 · 2019: 1 · 2018: 3
- FWCI
- 2.16
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Communications in Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Canadian Institute for Advanced Research
- Air Force Office of Scientific Research (FA9550-16-1- 0082)
- Simons Foundation
- 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
- approximate quantum error correction, EBIT, quantum channel capacity, state merging, entanglement distillation, remote state preparation, information leakage, entanglement-assisted capacity, quantum resource theory
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