TTMS28. Trace functions in quantum information theory
Speaker: Dr. Anna Vershynina, University of Houston, USA
Email: [email protected]
Abstract: We will discuss the convexity of several operator trace functions motivated by problems in quantum information theory. In particular, we will focus on the data processing inequality (or monotonicity) for several relative entropies. The inequality effectively states that quantum states become harder to distinguish after they pass through a noisy quantum channel. It has been shown that this inequality for some relative entropies is equivalent to convexity of certain trace functions. Additionally, the convexity of these trace functions gives rise to the conditions on states that ensure equality in the data processing inequality. I will report on the newest result by my collaborators and I on the convexity of a recently introduced operator trace function relevant to the data processing inequality for alpha-z Renyi relative entropy. I will present the full classification of its convexity and concavity region. Moreover, I will show that the convexity of two other well-known trace functions is not stable with the change of one parameter.