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The research of our group aims at fundamental and current questions of quantum theory, mainly concerning quantum information. Further we investigate the role of time in quantum mechanics. Below we list the main current and past research areas and give a short description of each.
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Quantum Cellular Automata
Quantum Cellular Automata (QCA) are (usually translation invariant) quantum operations on a lattice of quantum systems. Special QCA can be universal programmable quantum computers, while simpler ones can serve as a building block of quantum computation schemes with combined global and local control. We study in particular Clifford QCA, which use the Clifford group operations. Despite being classically simulatable, they generate highly entangled states used for measurement based quantum computation, and are a basic ingredient of many schemes for universal quantum computation with combined global and local control.
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Quantum Channels
Quantum Memory Channels and Quantum Convolutional Codes
Quantum memory channels are quantum operations, whose action depends on preceding uses. A central property of memorychannels is the so called "forgetfulness", which means that the influence of foregoing uses vanishes with an increasing number of channel uses. We are interested in the following questions: - Tomography of memory channels: Given an unknown channel. Under which assumptions is it possible, to determine the action of the channel on arbitrary input-states. What would be a protocol for such a tomography. - On the fly inversion of memory channels: In general a memory channel spreads the information given in single inputs (uses of the channel) to many outputs. We want to answer the question, under which circumstances and how we can recover the information with maximal fidelity, before we know all the outputs. - Convolutional codes: The spreading of information passing though memory channels to many outputs can be used to protect quantum information against errors. We investigate these convolutional error-correcting codes and their performance in comparison with block codes.
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Quantum Cryptography and Key Distribution
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Many-body systems
Many-body physics is concerned with the behaviour of large collections of
individual systems, subject to local interactions. While - in principle -
quantum mechanics allows for a complete treatment of such systems, it is often
the case that making even basic predictions is computationally intractable.
This inherit complexity gives rise to two complementary approaches. On the one
hand, it is of high interest to identify certain classes of many-body systems
which do allow for an efficient description, and for which predictions can be
made either analytically, or at least efficiently on a classical computer. On
the other hand, one may try to make a virtue of necessity: in this approach,
the goal is to devise quantum computing schemes that can utilize the
computational power of quantum systems to one's advantage.
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Foundations of Quantum Mechanics
Bell inequalities and independence
In quantum information it is well known, that a pair of maximally
entangled qubits maximally violates a Bell inequality of CHSH type. The
converse statement also holds, namely that only maximally entangled
qubits give maximal violation. We are investigating an extension of this
to near maximal violation and explore the bounds on the independence of
the quasi qubit subsystem from the environment. Results have application
to quantum cryptography in the context of device-independent security.
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Quantum Programming Languages
Quantum Programming Languages (QPLs) are formal systems which serve as a means to formulate quantum
algorithms and communication processes, in particular quantum cryptographic protocols, in a more accurate
way than is possible with verbatim texts or informal pseudocode. The goal is to transfer and extend
concepts of classical programming to quantum programming and quantum communication. In order to experiment
with a QPL the language system should be installed on top of a classical simulator. Therefore, in addition
to its close connection to quantum algorithms, research on QPLs is also closely related to the subject of
classical simulatability of quantum systems. For details and basic references look at this survey.
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Last modified: Fri, 23 Apr 2010
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