References

KSW2006

D. Kretschmann, D. Schlingemann, and R. F. Werner, “The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation” (2006). arXiv:quant-ph/0605009. Theorems 1 and 3, with their completely bounded norm conventions.

BenyOreshkov2010

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.

BenyOreshkov2011

C. Bény and O. Oreshkov, “Approximate simulation of quantum channels” (2011). arXiv:1103.0649.

KnillLaflamme1997

E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A 55, 900–911 (1997). doi:10.1103/PhysRevA.55.900. Preprint: arXiv:quant-ph/9604034.

Watrous2018

J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018). Author-hosted manuscript and errata: https://cs.uwaterloo.ca/ watrous/TQI/.

Hawking1975

S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics 43, 199–220 (1975). doi:10.1007/BF02345020.

BraunsteinPati2007

S. L. Braunstein and A. K. Pati, “Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox,” Physical Review Letters 98, 080502 (2007). doi:10.1103/PhysRevLett.98.080502. arXiv:gr-qc/0603046.

NakataWakakuwaKoashi2023

Y. Nakata, E. Wakakuwa, and M. Koashi, “Black holes as clouded mirrors: the Hayden–Preskill protocol with symmetry,” Quantum 7, 928 (2023). doi:10.22331/q-2023-02-21-928. arXiv:2007.00895.

FaistEtAl2020

P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous symmetries and approximate quantum error correction,” Physical Review X 10, 041018 (2020). doi:10.1103/PhysRevX.10.041018. arXiv:1902.07714.

Mathur2009

S. D. Mathur, “The information paradox: a pedagogical introduction,” Classical and Quantum Gravity 26, 224001 (2009). doi:10.1088/0264-9381/26/22/224001. arXiv:0909.1038.

MathurPlumberg2011

S. D. Mathur and C. Plumberg, “Correlations in Hawking radiation and the infall problem” (2011). arXiv:1101.4899.

AlmheiriEtAl2020

A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica wormholes and the entropy of Hawking radiation,” Journal of High Energy Physics 05 (2020), 013. doi:10.1007/JHEP05(2020)013. arXiv:1911.12333.

Penington2020

G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox.” arXiv:1905.08255, version 3 (2020).

EngelhardtWall2015

N. Engelhardt and A. C. Wall, “Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime,” Journal of High Energy Physics 01 (2015), 073. doi:10.1007/JHEP01(2015)073. arXiv:1408.3203.

PeningtonEtAl2022

G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, “Replica wormholes and the black hole interior.” arXiv:1911.11977. The cited preprint includes the Petz-map reconstruction discussion.

AlmheiriEngelhardtMarolfMaxfield2019

A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,” Journal of High Energy Physics 12 (2019), 063. doi:10.1007/JHEP12(2019)063. arXiv:1905.08762.

Page2013

D. N. Page, “Time Dependence of Hawking Radiation Entropy,” Journal of Cosmology and Astroparticle Physics 09 (2013), 028. arXiv:1301.4995.

CheungHawkA

N. Cheung, Hawk01-A, version 1, unpublished manuscript, n.d. Supplied source: exact constant-complement criterion, conserving completions, delayed-query optima, and complete observer/regulator interfaces. Labels include thm:complement, thm:completion, and thm:completionoptima. Source collection: Enter Calculus Companion.

CheungEm03A

N. Cheung, Em03-A, version 1, unpublished manuscript, n.d. Supplied source: fixed-background scalar emission law, thm:main, and finite-packet source normalization. Source collection: Enter Calculus Companion.

CheungEm03E

N. Cheung, Em03-E, version 1, unpublished manuscript, n.d. Supplied source descriptions: sequential key/transfer dynamics, complete complement, leakage, and referenced recovery. Supplied theorem excerpt: thm:recovery. Source collection: Enter Calculus Companion.

CheungEm05A

N. Cheung, Em05-A, version 1, unpublished manuscript, n.d. Supplied source: signed extraction isometry and complete complement, thm:channels; information and diagnostic separation interfaces. Source collection: Enter Calculus Companion.

CheungEm05B

N. Cheung, Em05-B, version 1, unpublished manuscript, n.d. Supplied source: exact constant-complement criterion, thm:constantComplement, and Bell-projection leakage witness, lem:leakageBell. Source collection: Enter Calculus Companion.

CheungEn02B

N. Cheung, En02-B, version 1, unpublished manuscript, n.d. Supplied source: resource-certified decoder soundness, thm:B1, and separation of observable, subsystem, and instrument tasks. Source collection: Enter Calculus Companion.

CheungEn02C

N. Cheung, En02-C, version 1, unpublished manuscript, n.d. Supplied source: finite sequential radiation recovery, thm:C2, and executable-access distinctions. Source collection: Enter Calculus Companion.

CheungEn02D

N. Cheung, En02-D, version 4, unpublished manuscript, n.d. Supplied source: energy-labelled unrestricted and capacity-limited recovery optima, thm:benchmark. Source collection: Enter Calculus Companion.

CheungEn02E

N. Cheung, En02-E, version 2, unpublished manuscript, n.d. Supplied source descriptions: finite Gaussian packets, complete occupation cutoffs, and calibrated recovery. Supplied theorem excerpt: thm:recovery. Source collection: Enter Calculus Companion.

CheungEn03A

N. Cheung, En03-A, version 1, unpublished manuscript, n.d. Supplied source: exact record compatibility, thm:pullback; residual-instrument, stability, and sampling interfaces. Source collection: Enter Calculus Companion.

CheungPsy02B

N. Cheung, Psy02-B, version 2, unpublished manuscript, n.d. Supplied source: complete-process equality and testing obstruction, thm:process. Source collection: Enter Calculus Companion.

CheungPsy03D

N. Cheung, Psy03-D, version 1, unpublished manuscript, n.d. Supplied source: carrier-independent uncued observation obstruction, cor:qobstruction. Source collection: Enter Calculus Companion.

CheungXIVI

N. Cheung, XIV-I, version 1, unpublished manuscript, n.d. Supplied source: constructed internal amplitude interface and unresolved full joint characteristic map, thm:I2, thm:I3. Source collection: Enter Calculus Companion.

CheungXIVJ

N. Cheung, XIV-J, version 1, unpublished manuscript, n.d. Supplied source: reconstruction descent, restricted supported-sector reference, unresolved full characteristic map, and no quantum admission, prop:descent, thm:reference, thm:J2, cor:noadmission. Source collection: Enter Calculus Companion.

CheungXVB

N. Cheung, XV-B, version 1, unpublished manuscript, n.d. Supplied source: conditional relative-lifting criterion, thm:lifting. Source collection: Enter Calculus Companion.