Entanglement wedge reconstruction using the Petz map

Chen, Chi-Fang; Penington, Geoffrey; Salton, Grant

doi:10.1007/jhep01(2020)168

Entanglement wedge reconstruction using the Petz map

Journal Article · Tue Jan 28 00:00:00 EST 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2020)168· OSTI ID:1803386

^[1]; ^[2]; Salton, Grant ^[3]

Stanford Univ., CA (United States). Dept. of Physics; OSTI
Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
Inst. for Quantum Information and Matter, Caltech, Pasadena, CA (United States)

At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension – no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0018407

OSTI ID:: 1803386

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2020; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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