Practical implementation of mutually unbiased bases using quantum circuits

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.Comment: 5 pages, 2 color figures. Comments welcome

Structure of the sets of mutually unbiased bases with cyclic symmetry

Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, since they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as the problem of finding a symmetric matrix over the field $\mathbb{F}_2$ equipped with an irreducible characteristic polynomial of a given Fibonacci index. The entanglement structure of the resulting complete sets is determined by two additive matrices of the same size.Comment: 20 page

High incidence of Angina pectoris in patients treated with 5-fluorouracil - A planned surveillance study with 102 patients

Objective: Angina pectoris, arrhythmic sudden death and myocardial infarction, all these cardiac events have occasionally been reported during 5-fluorouracil (5-FU) chemotherapy. Underlying mechanisms leading to these events are unknown; damage to the myocytes or vasospasms have been discussed. Methods: 102 consecutive and unselected patients were monitored with 12-lead ECG, echocardiography and radionuclide ventriculography prior to the first cycle of 5-FU chemotherapy and 3 months from baseline. Results: 19% of the patients developed reversible symptoms of angina pectoris during treatment which lasted up to 12 h after cessation of the infusion. Most of the 19 patients showed corresponding ECG changes. 6 out of the 19 patients with severe angina pectoris had subsequent coronary angiography. In none of these patients the coronary angiography showed coronary artery disease, but it showed low ventricular function (ejection fraction <50%) in 2 patients. The ejection fraction did not increase overtime. Arrhythmias were screened for with Holter monitoring during 5-FU chemotherapy. The frequency of bradycardia and ventricular extrasystoles increased significantly (p < 0.05) during treatment compared to arrhythmias in Holter monitoring 3 months later. Furthermore the Qtc time in the ECG 3 months later was significantly prolonged (p < 0.05) compared to baseline values. Conclusions:The incidence of angina pectoris in patients during 5-FU treatment seems higher than previously suspected. As myocardial ischemia can be fatal, attentiveness to these symptoms and immediate treatment are crucial. Copyright (C) 2003 S. Karger AG, Basel

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

WSPC- Proceedings Trim Size: 9in x 6in main 1 Characterizing Swing-Leg Retraction in Human Locomotion

contact, is observed in human locomotion. While several advantages of swingleg retraction, like gait stability and perturbation rejection, are shown by conceptual models, there is currently very little experimental data on swing-leg retraction in human motion. In this paper, kinematic data for twenty-eight subjects walking and running at different speeds are analyzed. Swing-leg retraction was shown to exist in walking and running at every non-zero speed. Additionally, swing-leg retraction speed and acceleration linearly increase with gait speed. At comparable gait speeds, swing-leg retraction speed is higher for running than for walking

Wigner function for SU(1,1)

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.Comment: Version accepted in Quantu

Direct observation of the quantum critical point in heavy fermion CeRhSi3_3

We report on muon spin rotation studies of the noncentrosymmetric heavy fermion antiferromagnet CeRhSi$_3$. A drastic and monotonic suppression of the internal fields, at the lowest measured temperature, was observed upon an increase of external pressure. Our data suggest that the ordered moments are gradually quenched with increasing pressure, in a manner different from the pressure dependence of the N\'eel temperature. At \unit{23.6}{kbar}, the ordered magnetic moments are fully suppressed via a second-order phase transition, and $T_{\rm{N}}$ is zero. Thus, we directly observed the quantum critical point at \unit{23.6}{kbar} hidden inside the superconducting phase of CeRhSi$_3$

Testosterone related to age and life-history stages in male baboons and geladas

AbstractDespite significant advances in our knowledge of how testosterone mediates life-history trade-offs, this research has primarily focused on seasonal taxa. We know comparatively little about the relationship between testosterone and life-history stages for non-seasonally breeding species. Here we examine testosterone profiles across the life span of males from three non-seasonally breeding primates: yellow baboons (Papio cynocephalus or P. hamadryas cynocephalus), chacma baboons (Papio ursinus or P. h. ursinus), and geladas (Theropithecus gelada). First, we predict that testosterone profiles will track the reproductive profiles of each taxon across their respective breeding years. Second, we evaluate age-related changes in testosterone to determine whether several life-history transitions are associated with these changes. Subjects include males (>2.5 years) from wild populations of each taxon from whom we had fecal samples for hormone determination. Although testosterone profiles across taxa were broadly similar, considerable variability was found in the timing of two major changes: (1) the attainment of adult levels of testosterone and (2) the decline in testosterone after the period of maximum production. Attainment of adult testosterone levels was delayed by 1 year in chacmas compared with yellows and geladas. With respect to the decline in testosterone, geladas and chacmas exhibited a significant drop after 3 years of maximum production, while yellows declined so gradually that no significant annual drop was ever detected. For both yellows and chacmas, increases in testosterone production preceded elevations in social dominance rank. We discuss these differences in the context of ecological and behavioral differences exhibited by these taxa