Universal recovery map for approximate Markov chains.
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that thequantum conditional mutual informationmeasures the performance of such recovery operations. More precisely, we prove that the conditional mutual informationI(A:C|B) of a tripartite quantum stateρABCcan be bounded from below by its distance to the closest recovered state [Formula: see text], where theC-part is reconstructed from theB-part only and the recovery map [Formula: see text] merely depends onρBC. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.
Institute for Theoretical Physics , ETH Zurich , Zurich, Switzerland.
David
D
Sutter
Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA; LIP, ENS de Lyon, Lyon, France.
Omar
O
Fawzi
Institute for Theoretical Physics , ETH Zurich , Zurich, Switzerland.
Renato
R
Renner
conditional mutual information; quantum Markov chains; recoverability; strong subadditivity