Stability theorem of depolarizing channels for the minimal output quantum Rényi entropiesWe show that the stability theorem of the depolarizing channel holds for the output quantum p-R\'enyi entropy for p≥2 or p=1, which is an extension of the well known case p=2. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum p-R\'enyi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate. University of Calgary, University of Alberta | Publication | 2016-01-01 | E. Bae, G. Gour, S. Lee, J. Park, B. C. Sanders |