The entropy power inequality with quantum conditioning
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The entropy power inequality with quantum conditioning. / de Palma, Giacomo.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 8, 08LT03, 2019.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The entropy power inequality with quantum conditioning
AU - de Palma, Giacomo
PY - 2019
Y1 - 2019
N2 - The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional entropy is minimum when the random variables are Gaussian. We prove the conditional entropy power inequality in the scenario where the conditioning system is quantum. The proof is based on the heat semigroup and on a generalization of the Stam inequality in the presence of quantum conditioning. The entropy power inequality with quantum conditioning will be a key tool of quantum information, with applications in distributed source coding protocols with the assistance of quantum entanglement.
AB - The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional entropy is minimum when the random variables are Gaussian. We prove the conditional entropy power inequality in the scenario where the conditioning system is quantum. The proof is based on the heat semigroup and on a generalization of the Stam inequality in the presence of quantum conditioning. The entropy power inequality with quantum conditioning will be a key tool of quantum information, with applications in distributed source coding protocols with the assistance of quantum entanglement.
U2 - 10.1088/1751-8121/aafff4
DO - 10.1088/1751-8121/aafff4
M3 - Journal article
VL - 52
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 8
M1 - 08LT03
ER -
ID: 213035308