The Ladder of Emergence N: Quantum Error Correction, Holographic Duality, and Information Recovery — A Cost Landscape Perspective on Quantum Information Dynamics

changzheng zhou, ZIQING zhou

Published May 7, 2026• 0 citations

Abstract

Central phenomena in quantum information processing– from the coding gainof quantum error-correcting codes, to the information mapping between boundaryand bulk in the AdS/CFT holographic duality, to the Page curve of informationrecovery during black hole evaporation– can be unified under the concept of “information compression cost”. This paper proposes that any quantum informationoperation must pay an irreversible entropy production jointly determined by Landauer’s principle and the Bekenstein bound, and that systems under these costconstraints seek to minimize a cost functional representing the difference betweendescription complexity and predictive (or protective) capability. The encodingprocess of stabilizer codes is modeled as the information compression required toprotect logical qubits against noise. The Ryu-Takayanagi formula in holographicduality indicates that the boundary theory must pay an information maintenancecost proportional to the area of the extremal surface in order to maintain its effective description of the bulk geometry. The Page curve of the black hole informationparadox is interpreted as a first-order kinetic phase transition on the cost landscapebetween two minima– one corresponding to an information-lost state and the otherto an information-recovered state. This framework integrates quantum error correction, the holographic principle, and the black hole information problem into aunified picture of information economics, and presents quantitative relations thatare amenable to further testing.

DOI: 10.5281/zenodo.20063742

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