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 non-trivial 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.
Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München（慕尼黑大学阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Physics and Astronomy, Western University（韦斯顿大学物理与天文学系）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）；Depto. de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid（马德里康普顿斯大学物理科学学院理论物理系）；Department of Physics, Shanghai University（上海大学物理系）
Approximate quantum error correction theory of non-isometric codes
Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
