Characterization of Majorization Monotone Quantum Dynamics

Majorization in Quantum Adiabatic Algorithms

We study the Majorization arrow in a big class of quantum adiabatic algorithms. In a quantum adiabatic algorithm, the ground state of the Hamiltonian is a guide state around which the actual state evolves. We prove that for any algorithm of this class, step-by-step majorization of the guide state holds perfectly. We also show that step-by-step majorization of the actual state appears if the run...

Operator Monotone Functions, Positive Definite Kernels and Majorization

Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is increasing w.r.t. the operator order, then for F (t) = ∫ f(t)dt the operator function F (X) is convex. Let h(t) and g(t) be C1 functions defined on an interval I. Suppose h(t) is non-decreasing and g(t) is increasing. Then we will define ...

Majorization and Matrix-Monotone Functions in Wireless Communications

Direct characterization of quantum dynamics.

The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative "direct characterization of quantum dynamics" (DCQD) algorithm. In contrast to all known QPT methods, this algorithm relies on error-detection techniques and does not require any quantum state tomogr...

Discrete Dynamics by Different Concepts of Majorization

For the description of complex dynamics of open systems, an approach is given by different concepts of majorization order structure . Discrete diffusion processes with both invariant object number and sink or source can be represented by the development of Young diagrams on lattices. As an experimental example, we investigated foam decay, dominated by sinks. The relevance of order structures fo...