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Daniel Burgarth (Erlangen-Nürnberg)
Dynamical Decoupling of Open Quantum Systems.
Dynamical Decoupling is a practical and generic method to reduce errors in quantum devices via a sequence of fast pulsed rotations. This is before error correction- the errors are (partially) prevented in the first place. The motivation is to get the physical error rate sufficiently low to be able to then use quantum error correction on top. While this is experimentally well established, relatively little is known theoretically on how efficient the method is when the environment Hamiltonian or the coupling to the environment is unbounded. I will report some recent work which provides us with bounds on the convergence speed of dynamical decoupling of unbounded operators.
Juan Manuel Pérez Pardo (Madrid)
Controlling the state of a quantum particle in a box by moving the walls.
I will present a quantum mechanical system consisting in a free particle trapped in a one-dimensional box. The position of the walls of the box can be changed by an external force. This system is governed by the non-autonomous Schrödinger equation. I will present a general analytical framework that can be used to study the controllability of theses systems. I will show that for any given initial and target states, there exists a movement of the walls that drives the initial state arbitrarily close to the target state.
This is joint work with A. Balmaseda and D. Lonigro
Eva-Maria Graefe (London)
Quantum and classical phase-space dynamics generated by non-Hermitian Hamiltonians.
While traditional quantum mechanics focusses on systems conserving energy and probability, described by Hermitian Hamiltonians, in recent years there has been ever growing interest in the use of non-Hermitian Hamiltonians. These can effectively describe loss and gain in a quantum system. In particular systems with a certain balance of loss and gain, so-called PT-symmetric systems, have attracted considerable attention. The first part of the talk will give a brief overview over motivations and interpretations of quantum systems with non-Hermitian Hamiltonians.
The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics beyond coherent states shows surprising features. Here we analyse the flow of the Husimi and Wigner phase-space distributions in a semiclassical limit, leading to a first order partial differential equation, that helps illuminate the foundations of the full quantum evolution. We discuss instructive examples, demonstrating how the full quantum dynamics unfolds on top of the “classical” flow.
This is based on joint work with Katherine Holmes, Simon Mallard, and Wasim Rehman.
Karol Życzkowski (Krakow)
Typical and atypical quantum structures: Which are more interesting?
We analyze the following quantum structures: the set $\Omega_N$ of mixed quantum states of order N, the set of discrete quantum operations (completely positive, trace preserving maps) acting on $\Omega_N$ and the set of Lindblad operators generating continuous dynamics in $\Omega_N$. On one hand, we investigate typical quantum states, operations and Lindblad operators. In each case their statistical properties, studied with suitable ensembles of random matrices, serve as reference points. On the other hand, we look for atypical quantum objects with extremal properties and identify some examples of highly entangled multipartite states and strongly entangling quantum gates. Furthermore, we analyze discrete structures in the Hilbert space, including quantum t-designs: collections of M objects, chosen in such a way that the average over them approximates the average over the measure analyzed for all functions of degree t. In particular, we demonstrate a link between projective designs (consisting of pure quantum states) with classical simplex designs, mixed states quantum designs and quantum operation designs.
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