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• W2894051297 abstract "The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened boundary of the region. If the interior of the region is lost after this compression, the full quantum state can be recovered to high precision by a quantum channel only acting on the thickened boundary. The thickness of the boundary scales inversely proportional to the error for arbitrary spin systems and logarithmically with the error for quasifree bosonic systems. Our results can be interpreted as a single-shot operational interpretation of the area law. The result for spin systems follows from a simple inequality showing that any probability distribution with entropy $S$ can be approximated to error $ϵ$ by a distribution with support of size $mathrm{exp}(S/ϵ)$, which we believe to be of independent interest. We also discuss an emergent approximate correspondence between bulk and boundary operators and the relation of our results to tensor network states." @default.
• W2894051297 created "2018-10-05" @default.
• W2894051297 creator A5039471780 @default.
• W2894051297 creator A5053630692 @default.
• W2894051297 date "2019-05-15" @default.
• W2894051297 modified "2023-10-12" @default.
• W2894051297 title "Single-Shot Holographic Compression from the Area Law" @default.
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• W2894051297 doi "https://doi.org/10.1103/physrevlett.122.190501" @default.
• W2894051297 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/31144922" @default.
• W2894051297 hasPublicationYear "2019" @default.
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