Prof Vlatko Vedral FInstP

Abstract:

When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state projective Hilbert space. A correction term to this geometric phase, in addition to the local subsystem phases, may appear from correlations between the subsystems. We find that this correction term can be characterized completely either by the entanglement or by the classical correlations for several classes of entangled state. States belonging to the former set are W states and their mixtures, while members of the latter set are cluster states, GHZ states and two classes of bound entangled state. We probe the structures of these states more finely using local invariants and suggest that the cause of the entanglement correction is a recently introduced gauge field-like SL(2,)-invariant called twist. © 2009 World Scientific Publishing Company.

Abstract:

We define and analyse the concept of entanglement production during the evolution of a general quantum mechanical dissipative system. While it is important to minimise entropy production in order to achieve thermodynamical efficiency, maximising the rate of change of entanglement is important in quantum information processing. Quantitative relations are obtained between entropy and entanglement productions, under specific assumptions detailed in the text. We apply these to the processes of dephasing and decay of correlations between two initially entangled qubits. Both the Master equation treatment as well as the higher Hilbert space analysis are presented. Our formalism is very general and contains as special cases many reported individual instance of entanglement dynamics, such as, for example, the recently discovered notion of the sudden death of entanglement. © 2009 IOP Publishing Ltd.

Abstract:

Here, we compare the critical behaviour of the ground state and the thermal state of the XX model. We analyze full energy spectra and the exact form of eigenstates to reconstruct the ground state and the thermally excited state. With the solutions, we discuss the properties of quantum phase transition at zero temperature as well as the state in a thermal equilibrium. © 2009 World Scientific Publishing Company.