Quantum limit theorems

Limit theorems for quantum entropies

Central Limit Theorems for Open Quantum Random Walks∗

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory (such as the well-known Hadamard random...

Limit theorems for discrete-time quantum walks on trees

We consider a discrete-time quantum walk Wt given by the Grover transformation on the Cayley tree. We reduce Wt to a quantum walk Xt on a half line with a wall at the origin. This paper presents two types of limit theorems for Xt. The first one is Xt as t → ∞, which corresponds to a localization in the case of an initial qubit state. The second one is Xt/t as t → ∞, whose limit density is given...

Entropy and Limit Theorems

I hereby declare that my thesis entitled`Entropy and Limit Theo-rems' is not substantially the same as any that I have submitted for a degree or diploma or other qualiication at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualiication. Chapter 3 extends results from a paper co-written w...

Some Limit Theorems