FOPRA Experiment 41: Entanglement-Breaking Evolutions
Course 0000005390 in SS 2021
|Course Type||practical training|
|Semester Weekly Hours||1 SWS|
Michael Marc Wolf
Assignment to Modules
Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.
|additional remarks||Entanglement is a fundamental resource in quantum information that features in many well-known protocols (e.g., teleportation). Therefore, it is of interest to understand which evolutions of quantum systems preserve or destroy this resource. In this project, you will investigate so-called entanglement-breaking maps, i.e., maps that for any input state produce a separable output. You will focus on physical situations where the interactions between an open system under consideration and its environment are weak so that the dynamics can be well described by a Markovian evolution. In mathematical terms, this means that you will study (continuous) semigroups of quantum channels. In this project, you will ﬁrst learn about basic properties of the objects of interest (i.e., entanglement-breaking channels and semigroups of channels) by solving a collection of mathematical exercises. Once you are familiar with these notions and after some technical preparation, you will be guided through the proof of the following equivalence, which is the main goal of the project: An evolution described by a semigroup of quantum channels becomes entanglement-breaking after some ﬁnite time if and only if every initial state converges to a unique full-rank invariant state. Your task will be to provide the details for the steps of the proof based on the instructions given. In doing so, you will encounter techniques from di↵erent areas relevant to quantum information, e.g., linear algebra and spectral theory. In particular, you will have an opportunity to apply what you have learned in the lecture on “Introduction to Quantum Information Processing”. This will give you a better understanding of the structure of the set of separable states, of the behaviour of Markovian quantum evolutions, and it will bring you closer to the current research about these questions.|