Prof Vlatko Vedral FInstP

Abstract:

We investigate entanglement properties of mixtures of short-range spin- s dimer coverings in lattices of arbitrary topology and dimension. We show that in one spatial dimension nearest neighbor entanglement exists for any spin s. Surprisingly, in higher spatial dimensions there is a threshold value of spin s below which the nearest neighbor entanglement disappears. The traditional "classical" limit of large spin value corresponds to the highest nearest neighbor entanglement that we quantify using the negativity. © 2007 The American Physical Society.

Abstract:

We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely multipartite entangled, while there is only a negligible amount of two-site entanglement. We comment on possible physical implications of our findings.

Abstract:

A different way to realize nonadiabatic geometric quantum computation is proposed by varying parameters in the Hamiltonian for nuclear-magnetic resonance, where the dynamical and geometric phases are implemented separately without the usual operational process. Therefore the phase accumulated in the geometric gate is a pure geometric phase for any input state. In comparison with the conventional geometric gates by rotating operations, our approach simplifies experimental implementations making them robust to certain experimental errors. In contrast to the unconventional geometric gates, our approach distinguishes the total and geometric phases and offers a wide choice of the relations between the dynamical and geometric phases. © 2007 The American Physical Society.

Abstract:

When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show that the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical phases of its subsystems. In contrast, the equivalent statement for the geometric phase is not generally true unless the state is separable. For an entangled state an additional term is present, the mutual geometric phase, that measures the change the additional correlations present in the entangled state make to the geometry of the state space. For N qubit states we find that this change can be explained solely by classical correlations for states with a Schmidt decomposition and solely by quantum correlations for W states. © 2007 The American Physical Society.