Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)

We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set of states annihilated by all invariant polynomials, and also the so called third secant variety, which can be interpreted as the generalization of GHZ-states for more than three qubits. All our geometric descriptions go along with algorithms which allow us to identify any given state in the nullcone or in the third secant variety as a point of one of the 47 varieties described in the paper. These 47 varieties correspond to 47 non-equivalent entanglement patterns, which reduce to 15 different classes if we allow permutations of the qubits.Comment: 48 pages, 7 tables, 13 figures, references and remarks added (v2

Pump induced Autler-Townes effect and A-T mixing in a four level atoms

It is shown by theoretical simulation that tuning of the pump power can induce mixing and crossing of Autler-Townes(A-T)components of closely spaced transitions in atoms. Pump radiation also leads to small shifts of the central hole of A-T doublet. Off-resonance pumping gives an asymmetry in the A-T components and by controlling pump frequency detuning it is also possible to mix the A-T components.Comment: 10 Pages, 3 figur

Psychiatric profiles of mothers who take Ecstasy/MDMA during pregnancy: Reduced depression 1 year after giving birth and quitting Ecstasy

Background: The recreational drug MDMA (3,4-methylenedioxymethamphetamine) or ‘Ecstasy’ is associated with heightened psychiatric distress and feelings of depression. The Drugs and Infancy Study (DAISY) monitored the psychiatric symptom profiles of mothers who used Ecstasy/MDMA while pregnant, and followed them over the first year post-partum. Methods: We compared 28 young women whom took MDMA during their pregnancy with a polydrug control group of 68 women who took other psychoactive drugs while pregnant. The Brief Symptom Inventory (BSI) was completed for several periods: The first trimester of pregnancy; and 1, 4 and 12 months after childbirth. Recreational drug use was monitored at each time point. Results: During the first trimester of pregnancy, MDMA-using mothers reported higher depression scores than the polydrug controls. At 1 year after childbirth, their BSI depression scores were significantly lower, now closer to the control group values. At the same time point, their self-reported use of MDMA became nearly zero, in contrast to their continued use of Cannabis/marijuana, nicotine and alcohol. We found significant symptom reductions in those with BSI obsessive-compulsive and interpersonal sensitivity, following Ecstasy/MDMA cessation. Conclusions: The findings from this unique prospective study of young recreational drug-using mothers are consistent with previous reports of improved psychiatric health after quitting MDMA

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Finite temperature quantum simulation of stabilizer Hamiltonians

We present a scheme for robust finite temperature quantum simulation of stabilizer Hamiltonians. The scheme is designed for realization in a physical system consisting of a finite set of neutral atoms trapped in an addressable optical lattice that are controllable via 1- and 2-body operations together with dissipative 1-body operations such as optical pumping. We show that these minimal physical constraints suffice for design of a quantum simulation scheme for any stabilizer Hamiltonian at either finite or zero temperature. We demonstrate the approach with application to the abelian and non-abelian toric codes.Comment: 13 pages, 2 figure

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Voltage rectification by a SQUID ratchet

We argue that the phase across an asymmetric dc SQUID threaded by a magnetic flux can experience an effective ratchet (periodic and asymmetric) potential. Under an external ac current, a rocking ratchet mechanism operates whereby one sign of the time derivative of the phase is favored. We show that there exists a range of parameters in which a fixed sign (and, in a narrower range, even a fixed value) of the average voltage across the ring occurs, regardless of the sign of the external current dc component.Comment: 4 pages, 4 EPS figures, uses psfig.sty. Revised version, to appear in Physical Review Letters (26 August 1996