The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference

Diamonds and the Mantle Geodynamics of Carbon: Deep Mantle Carbon Evolution from the Diamond Record

The science of studying diamond inclusions for understanding Earth history has developed significantly over the past decades, with new instrumentation and techniques applied to diamond sample archives revealing the stories contained within diamond inclusions. This chapter reviews what diamonds can tell us about the deep carbon cycle over the course of Earth’s history. It reviews how the geochemistry of diamonds and their inclusions inform us about the deep carbon cycle, the origin of the diamonds in Earth’s mantle, and the evolution of diamonds through time

Diamonds and the mantle geodynamics of carbon:deep mantle carbon evolution from the diamond record

The science of studying diamond inclusions for understanding Earth history has developed significantly over the past decades, with new instrumentation and techniques applied to diamond sample archives revealing the stories contained within diamond inclusions. This chapter reviews what diamonds can tell us about the deep carbon cycle over the course of Earth’s history. It reviews how the geochemistry of diamonds and their inclusions inform us about the deep carbon cycle, the origin of the diamonds in Earth’s mantle, and the evolution of diamonds through time

Diamonds and the mantle geodynamics of carbon : deep mantle carbon evolution from the diamond record

SBS and EHH for support from the US National Science Foundation (EAR-104992); FN and PN for support from the European Research Council Starting Grant (#307322); Wuyi Wang and Tom Moses of the Gemological Institute of America (GIA) for the support of the research projects undertaken by KVS and EMS; and SCK for the support of De Beers Technologies. This is contribution 1168 from the ARC Centre of Excellence for Core to Crust Fluid Systems (www.ccfs.mq.edu.au) and 1130 in the Geochemical Evolution and Metallogeny of the Continents Key Centre (www.gemoc.mq.edu.au).The science of studying diamond inclusions for understanding Earth history has developed significantly over the past decades, with new instrumentation and techniques applied to diamond sample archives revealing the stories contained within diamond inclusions. This chapter reviews what diamonds can tell us about the deep carbon cycle over the course of Earth’s history. It reviews how the geochemistry of diamonds and their inclusions inform us about the deep carbon cycle, the origin of the diamonds in Earth’s mantle, and the evolution of diamonds through time.Publisher PD