Title: Randomness and one-shot decoupling in quantum information science
Reporter: Yoshifumi Nakata Project researcher (The University of Tokyo)
Time: 2017-12-22 (Friday) 10:00
Abstract: Randomness is often very useful in information processing. This is true even in the quantum regime, where randomness is described by a random unitary uniformly distributed with respect to the Haar measure. In this talk, we begin with a brief review of the so-called one-shot decoupling, one of the most important applications of a Haar random unitary in quantum information theory. We then turn to one-shot decoupling with unitaries less random than the Haar ones. We especially consider decoupling with "unitary t-designs", random unitaries simulating Haar random ones up to the t-th order moments. It was known that good approximations of unitary 2-designs are sufficient for decoupling. Here, we show that rather bad approximations of unitary 2-designs suffice. Our result raises interesting questions: how much randomness is needed for decoupling, and more fundamentally, how can we define random unitaries which are less random than 2-designs?