A remainder term for Holder's inequality for matrices and quantum entropy inequalities

作者：Carlen Eric A^*

来源：ARCHIV DER MATHEMATIK, 2017, 109(4): 365-371.

DOI：10.1007/s00013-017-1066-8

• Density matrix
• Entropy
• Uniform convexity

We prove a sharp remainder term for Holder's inequality for traces as a consequence of the uniform convexity properties of the Schatten trace norms. We then show how this implies a novel family of Pinsker type bounds for the quantum Renyi entropy. Finally, we show how the sharp form of the usual quantum Pinsker inequality for relative entropy may be obtained as a fairly direct consequence of uniform convexity.

• 出版日期2017-10
• 单位rutgers