Speaker
B V Rajarama Bhat, Indian Statistical Institute, Bangalore
Abstract
Unital quantum channels serve as the quantum analogue of doubly stochastic maps. The most accessible examples of these channels are mixed unitary maps—those expressible as convex combinations of unitary conjugations. In this talk, we establish that both discrete and continuous semigroups of unital quantum channels are eventually mixed unitary. This result is surprising even in the restricted case of Schur maps, and it contrasts sharply with the resolution of the asymptotic quantum Birkhoff conjecture. While Haagerup and Musat demonstrated that tensor powers of certain unital channels maintain a persistent positive distance from the set of mixed unitary maps, our findings reveal that this gap vanishes in finite time when considering the evolution of ordinary powers within a semigroup. Define the mixed unitary index of a unital channel as the as the threshold power such that all subsequent powers are mixed unitary. For any fixed dimension d>3, we demonstrate that no universal upper bound exists for this index. Finally, we discuss why characterizing the regions of mixed unitarity for semigroups of quantum doubly stochastic maps remains a challenge. This talk is based on a joint work with R. Devendra, which builds upon some recent results by D. Kribs, J. Levick, R. Pereira and M. Rahaman.
B V Rajarama Bhat, Indian Statistical Institute, Bangalore
Abstract
Unital quantum channels serve as the quantum analogue of doubly stochastic maps. The most accessible examples of these channels are mixed unitary maps—those expressible as convex combinations of unitary conjugations. In this talk, we establish that both discrete and continuous semigroups of unital quantum channels are eventually mixed unitary. This result is surprising even in the restricted case of Schur maps, and it contrasts sharply with the resolution of the asymptotic quantum Birkhoff conjecture. While Haagerup and Musat demonstrated that tensor powers of certain unital channels maintain a persistent positive distance from the set of mixed unitary maps, our findings reveal that this gap vanishes in finite time when considering the evolution of ordinary powers within a semigroup. Define the mixed unitary index of a unital channel as the as the threshold power such that all subsequent powers are mixed unitary. For any fixed dimension d>3, we demonstrate that no universal upper bound exists for this index. Finally, we discuss why characterizing the regions of mixed unitarity for semigroups of quantum doubly stochastic maps remains a challenge. This talk is based on a joint work with R. Devendra, which builds upon some recent results by D. Kribs, J. Levick, R. Pereira and M. Rahaman.