Quantum minimal surfaces from quantum error correction
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow; in particular, w...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2022-05-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.12.5.157 |
| _version_ | 1817988661638070272 |
|---|---|
| author | Chris Akers, Geoff Penington |
| author_facet | Chris Akers, Geoff Penington |
| author_sort | Chris Akers, Geoff Penington |
| collection | DOAJ |
| description | We show that complementary state-specific reconstruction of logical (bulk)
operators is equivalent to the existence of a quantum minimal surface
prescription for physical (boundary) entropies. This significantly generalizes
both sides of an equivalence previously shown by Harlow; in particular, we do
not require the entanglement wedge to be the same for all states in the code
space. In developing this theorem, we construct an emergent bulk geometry for
general quantum codes, defining "areas" associated to arbitrary logical
subsystems, and argue that this definition is "functionally unique." We also
formalize a definition of bulk reconstruction that we call "state-specific
product unitary" reconstruction. This definition captures the quantum error
correction (QEC) properties present in holographic codes and has potential
independent interest as a very broad generalization of QEC; it includes most
traditional versions of QEC as special cases. Our results extend to approximate
codes, and even to the "non-isometric codes" that seem to describe the interior
of a black hole at late times. |
| first_indexed | 2024-04-14T00:36:55Z |
| format | Article |
| id | doaj.art-72ac756761f94e9c97e76a85886b218a |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-14T00:36:55Z |
| publishDate | 2022-05-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-72ac756761f94e9c97e76a85886b218a2022-12-22T02:22:20ZengSciPostSciPost Physics2542-46532022-05-0112515710.21468/SciPostPhys.12.5.157Quantum minimal surfaces from quantum error correctionChris Akers, Geoff PeningtonWe show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining "areas" associated to arbitrary logical subsystems, and argue that this definition is "functionally unique." We also formalize a definition of bulk reconstruction that we call "state-specific product unitary" reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases. Our results extend to approximate codes, and even to the "non-isometric codes" that seem to describe the interior of a black hole at late times.https://scipost.org/SciPostPhys.12.5.157 |
| spellingShingle | Chris Akers, Geoff Penington Quantum minimal surfaces from quantum error correction SciPost Physics |
| title | Quantum minimal surfaces from quantum error correction |
| title_full | Quantum minimal surfaces from quantum error correction |
| title_fullStr | Quantum minimal surfaces from quantum error correction |
| title_full_unstemmed | Quantum minimal surfaces from quantum error correction |
| title_short | Quantum minimal surfaces from quantum error correction |
| title_sort | quantum minimal surfaces from quantum error correction |
| url | https://scipost.org/SciPostPhys.12.5.157 |
| work_keys_str_mv | AT chrisakersgeoffpenington quantumminimalsurfacesfromquantumerrorcorrection |