Details
| Original language | English |
|---|---|
| Article number | 020501 |
| Journal | Physical review letters |
| Volume | 119 |
| Issue number | 2 |
| Publication status | Published - 14 Jul 2017 |
| Externally published | Yes |
Abstract
While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.
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In: Physical review letters, Vol. 119, No. 2, 020501, 14.07.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Towards Holography via Quantum Source-Channel Codes
AU - Pastawski, Fernando
AU - Eisert, Jens
AU - Wilming, Henrik
PY - 2017/7/14
Y1 - 2017/7/14
N2 - While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.
AB - While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.
UR - http://www.scopus.com/inward/record.url?scp=85025445661&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.119.020501
DO - 10.1103/PhysRevLett.119.020501
M3 - Article
C2 - 28753372
AN - SCOPUS:85025445661
VL - 119
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 2
M1 - 020501
ER -