Michael Wolf

Mathematical Physics

Technical University Munich

Zentrum Mathematik, M5

Boltzmannstrasse 3

85748 Garching

+49 89 289-17002

m.wolf[at]tum.de

Group Webpage

Description

Research focus: quantum information, quantum many-body physics, mathematical foundations

Our team works on the mathematical and conceptual foundations of quantum theory. From the rigorous perspective of mathematical physics we are interested in the unimagined possibilities the world of quantum theory has in store for us. The main research directions of our group are summarized in the following.


Quantum Channels

Quantum Channels are the quantum counterparts of classical Markov chains and describe quantum evolutions and processes in general. The analysis of the mathematical structure of these objects is the backbone of our research.


Quantum Shannon Theory

Quantum Shannon Theory aims at putting Shannon's mathematical theory of communication on the general grounds of quantum theory. We are particularly interested in determining optimal communication rates and in the analysis of non-additivity effects, i.e., the possibility of increasing communication rates by exploiting entanglement.


Quantum Spin Lattices

Quantum spin lattices are effective models for condensed matter systems. At low temperature they exhibit interesting properties due to quantum correlations, which we try to understand - often based on tensor networks.


Quantum Measurements

We are interested in how measurements in general and information extraction in particular disturb a quantum system. On the other hand, we are investigating efficient ways of information extraction. The latter also concerns scenarios where the effective dimension is considerably smaller than the one used to describe the system at hand and the question is, how and when this fact can be exploited.


Other topics addressed in our group concern: entanglement theory, quantum thermodynamics, decidability questions in quantum many-body physics and information theory, Bell inequalities and continuous variable systems, especially quasi-free systems. Close collaborations exist with UC Madrid, DAMTP Cambridge, MPQ Garching, ETH Zurich, KU Copenhagen and other groups.

Publications

Quantum Zeno effect generalized

T. Möbus, M. Wolf.

Journal of Mathematical Physics 60, 052201 (2019).

Show Abstract

The quantum Zeno effect, in its original form, uses frequent projective measurements to freeze the evolution of a quantum system that is initially governed by a fixed Hamiltonian. We generalize this effect simultaneously in three directions by allowing open system dynamics, time-dependent evolution equations and general quantum operations in place of projective measurements. More precisely, we study Markovian master equations with bounded generators whose time dependence is Lipschitz continuous. Under a spectral gap condition on the quantum operation, we show how frequent measurements again freeze the evolution outside an invariant subspace. Inside this space, the evolution is described by a modified master equation.

DOI: 10.1063/1.5090912

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