References

BenyKempfKribs

C. Bény, A. Kempf, and D. W. Kribs, “Generalization of quantum error correction via the Heisenberg picture,” Physical Review Letters 98, 100502 (2007). doi:10.1103/PhysRevLett.98.100502. arXiv:quant-ph/0608071.

BenyKempfKribsPRA

C. Bény, A. Kempf, and D. W. Kribs, “Quantum error correction of observables,” Physical Review A 76, 042303 (2007). doi:10.1103/PhysRevA.76.042303.

BenyOreshkov

C. Bény and O. Oreshkov, “General conditions for approximate quantum error correction and near-optimal recovery channels,” Physical Review Letters 104, 120501 (2010). doi:10.1103/PhysRevLett.104.120501. arXiv:0907.5391.

PastawskiEtAl

F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill, “Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence,” Journal of High Energy Physics 2015(06), 149 (2015). doi:10.1007/JHEP06(2015)149. arXiv:1503.06237.

LaflammeEtAl

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correction code,” Physical Review Letters 77, 198–201 (1996). doi:10.1103/PhysRevLett.77.198. arXiv:quant-ph/9602019.

WallmanFlammia

J. J. Wallman and S. T. Flammia, “Randomized benchmarking with confidence,” arXiv:1404.6025v4 (2015). The supplied version is used for its normalized Choi convention, diamond-distance bounds, and finite-sampling qualifications. arXiv:1404.6025.

Watrous

J. Watrous, “Simpler semidefinite programs for completely bounded norms,” arXiv:1207.5726. arXiv:1207.5726.

Hoeffding

W. Hoeffding, “Probability inequalities for sums of bounded random variables,” Journal of the American Statistical Association 58(301), 13–30 (1963). doi:10.1080/01621459.1963.10500830.

ClopperPearson

C. J. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika 26(4), 404–413 (1934). doi:10.1093/biomet/26.4.404.

CheungEn02B

N. Cheung, internal manuscript identifier En02-B. Attribution and theorem-role descriptions supplied in Oai280-C ref.txt; full text and publication metadata not supplied. Cited for provenance only.

CheungEn02C

N. Cheung, internal manuscript identifier En02-C. Attribution and theorem-role descriptions supplied in Oai280-C ref.txt; full text and publication metadata not supplied. Cited for provenance only.

CheungEn05C

N. Cheung, internal manuscript identifier En05-C. The supplied notes associate this identifier with snapshot determination and adjoint containment. Full text and publication metadata not supplied.

CheungIEn06A

N. Cheung, internal manuscript identifiers I and En06-A. The supplied notes associate them with classical-record and entanglement-breaking obstructions. Full texts and publication metadata not supplied.

CheungVIIG

N. Cheung, internal manuscript identifier VII-G. The supplied notes associate it with the full-code constant-complement criterion and spectator conventions. Full text and publication metadata not supplied.

CheungOai265B

N. Cheung, internal manuscript identifier Oai265-B. The supplied notes associate it with complete validation contracts, branch accounting, and finite-confidence certification. Full text and publication metadata not supplied.

CheungOai290A

N. Cheung, internal manuscript identifier Oai290-A. The supplied notes associate it with effect/channel separation, specified-decoder certification, and three-way decisions. Full text and publication metadata not supplied.

CheungEm05B

N. Cheung, internal manuscript identifier Em05-B. The supplied notes associate it with complete instruments, failure branches, complementary leakage, and full-code recovery. Full text and publication metadata not supplied.

CheungXVIIA

N. Cheung, internal manuscript identifier XVII-A. The supplied notes associate it with typed operator and channel targets and the separation from entanglement-wedge claims. Full text and publication metadata not supplied.

CheungOai280AB

N. Cheung, internal manuscript identifiers Oai280-A and Oai280-B. The supplied notes associate them with finite access, patch recovery, task counterexamples, and certificate-specific shot limitations. Full texts and publication metadata not supplied.

CheungEn07B

N. Cheung, internal manuscript identifier En07-B. The supplied notes report additional same-model endpoint obligations. Their full statements, full text, and publication metadata were not supplied; they are not premises of this paper.