TY - JOUR
T1 - How not to Rényi-generalize the quantum conditional mutual information
AU - Erker, Paul
PY - 2015/7/10
Y1 - 2015/7/10
N2 - © 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.
AB - © 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.
KW - non-i.i.d.
KW - quantum conditional mutual information
KW - quantum information theory
KW - Rényi divergences
U2 - 10.1088/1751-8113/48/27/275303
DO - 10.1088/1751-8113/48/27/275303
M3 - Article
SN - 1751-8113
VL - 48
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 27
M1 - 275303
ER -