Prof Vlatko Vedral FInstP

Abstract:

By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior. © 2007 Elsevier B.V. All rights reserved.

Abstract:

We present a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground-state entanglement. The condition is written in terms of the ground-state entanglement and the partition function and it gives transition temperatures below which entanglement is guaranteed to survive. It is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Examples where the condition is calculated are given. These examples allow us to characterize a minimum gapping behavior for the survival of entanglement in the thermodynamic limit. Further, the same technique can be used to find noise thresholds in the generation of useful resource states for one-way quantum computing. © Europhysics Letters Association.

Abstract:

In this paper we argue that one-way quantum computation can be seen as a form of phase transition with the available information about the solution of the computation being the order parameter. We draw a number of striking analogies between standard thermodynamical quantities such as energy, temperature, work, and corresponding computational quantities such as the amount of entanglement, time, potential capacity for computation, respectively. Aside from being intuitively pleasing, this picture allows us to make novel conjectures, such as an estimate of the necessary critical time to finish a computation and a proposal of suitable architectures for universal one-way computation in 1D. © 2008 Springer Science+Business Media, LLC.

Abstract:

The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantized Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties. We define the corresponding prefix complexity and show that the inequalities obeyed by this prefix complexity are also obeyed by von Neumann entropy. © 2008 World Scientific Publishing Company.