Events Calendar

Markovian Evolution of a Quantum Ensemble and its Long-Term Behavior

Speaker: Min-Hsiu Hsieh, University of Technology, Sydney

Talk Title: Markovian Evolution of a Quantum Ensemble and its Long-Term Behavior

Abstract: We extend the theory of quantum Markov processes on a single quantum state to a broader theory that covers Markovian evolution of an ensemble of quantum states. This generalizes Lindblad's formulation of quantum dynamical semigroups. Our formalism includes an explicit form of semigroups, their time derivative-” the infinitesimal generator, a carr'e du champ operator, and matrix *phi-entropy. We find a matrix *phi-Sobolev inequality that governs the exponential decay of the these matrix *phi-entropy. Special cases of the matrix *phi-entropy evaluate to the Holevo quantity and the variance of the ensemble, which allows us to relate our formalism to classical coding over quantum channels. In particular, we show that the convergence rates of two special semigroups-the depolarizing and phase-damping channels-can be explicitly computed. They result in fundamentally different equilibrium situations, for which there is no classical analogy.

Biography: Min-Hsiu Hsieh received his PhD degree in electrical engineering from the University of Southern California, Los Angeles, in 2008. From 2008-2010, he was a Researcher at the ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, Tokyo, Japan. From 2010-2012, he was a Postdoctoral Researcher at the Statistical Laboratory, the Centre for Mathematical Sciences, the University of Cambridge, UK. He is now an Future Fellow and Associate Professor at the Centre for Quantum Computation & Intelligent Systems (QCIS), Faculty of Engineering and Information Technology (FEIT), University of Technology, Sydney (UTS). His scientific interests include quantum Shannon theory, entanglement theory, and quantum coding theory.

Host: Todd Brun, x03503, tbrun@usc.edu

Location: Hughes Aircraft Electrical Engineering Center (EEB) - 539

Audiences: Everyone Is Invited

Contact: Gerrielyn Ramos