Optimal observables to determine entanglement of a two qubit state

Experimental determination of entanglement is important not only to characterize the state and use it in quantum information, but also in understanding complicated phenomena such as phase transitions. In this paper we show that in many cases, it is possible to determine entanglement of a two qubit state, as represented by concurrence, with a few observables, most of which are local. In particular, rank 1 and rank 2 states need exclusively measurement of local observables while rank 3 states need measurement of just one correlation observable in addition to local observables. Only the rank 4 states are shown to require a more detailed tomography. The analysis also sheds light on the other measure, non separability since it is a lower bound on concurrence.Comment: 8 pages, 1 figur

A Fast Eigen Solution for Homogeneous Quadratic Minimization with at most Three Constraints

We propose an eigenvalue based technique to solve the Homogeneous Quadratic Constrained Quadratic Programming problem (HQCQP) with at most 3 constraints which arise in many signal processing problems. Semi-Definite Relaxation (SDR) is the only known approach and is computationally intensive. We study the performance of the proposed fast eigen approach through simulations in the context of MIMO relays and show that the solution converges to the solution obtained using the SDR approach with significant reduction in complexity.Comment: 15 pages, The same content without appendices is accepted and is to be published in IEEE Signal Processing Letter

Knowledge Reuse for Customization: Metamodels in an Open Design Community for 3d Printing

Theories of knowledge reuse posit two distinct processes: reuse for replication and reuse for innovation. We identify another distinct process, reuse for customization. Reuse for customization is a process in which designers manipulate the parameters of metamodels to produce models that fulfill their personal needs. We test hypotheses about reuse for customization in Thingiverse, a community of designers that shares files for three-dimensional printing. 3D metamodels are reused more often than the 3D models they generate. The reuse of metamodels is amplified when the metamodels are created by designers with greater community experience. Metamodels make the community's design knowledge available for reuse for customization-or further extension of the metamodels, a kind of reuse for innovation