We construct steering inequalities which exhibit unbounded violation. The concept was to exploit the relationship between steering violation and uncertainty relation. To this end we apply mutually unbiased bases and anti-commuting observables, known
to exibit the strongest uncertainty. In both cases, we are able to procure unbounded violations. Our approach is much more constructive and transparent than the operator space theory approach employed to obtain large violation of Bell inequalities. Importantly, using anti-commuting observables we are able to obtain a {it dichotomic} steering inequality with unbounded violation. So far there is no analogous result for Bell inequalities. Interestingly, both the dichotomic inequality and one of our inequalities can not be directly obtained from existing uncertainty relations, which strongly suggest the existence of an unknown kind of uncertainty relation.
A local numerical range is analyzed for a family of circulant observables and states of composite $2 otimes d$ systems. It is shown that for any $2otimes d$ circulant operator $cal O$ there exists a basis giving rise to the matrix representation with
real non-negative off-diagonal elements. In this basis the problem of finding extremum of $cal O$ on product vectors $ket{x}otimes ket{y} in mathbb{C}^2otimes mathbb{C}^d$ reduces to the corresponding problem in $mathbb{R}^2otimes mathbb{R}^d$. The final analytical result for $d=2$ is presented.
We present the results of a photometric campaign of the dwarf nova V1040 Cen. The light curve shows two normal outbursts with recurrence time ~ 40 days and amplitude ~ 2.5 mag. Quiescence data show oscillations with periods in the range ~ 0.1 days (2
.4 h) to ~ 0.5 days (12 h) of unknown origin. We measured the orbital period of V1040 Cen to be P_orb=0.060458(80) days (1.451+-0.002 h). Based on the M_v-P_orb relation we found the distance of V1040 Cen to be 137+-31 pc. In this paper we also report the detection of eleven new variable stars in the field of the monitored dwarf nova.
We report extensive photometry of the dwarf nova V419 Lyr throughout its 2006 July superoutburst till quiescence. The superoutburst with amplitude of ~3.5 magnitude lasted at least 15 days and was characterized by the presence of clear superhumps wit
h a mean period of Psh=0.089985(58) days (129.58+-0.08 min). According to the Stolz-Schoembs relation, this indicates that the orbital period of the binary should be around 0.086 days i.e. within the period gap. During the superoutburst the superhump period was decreasing with the rate of dotP/Psh=-24.8(2.2)*10^-5, which is one of the highest values ever observed in SU UMa systems. At the end of the plateau phase, the superhump period stabilized at a value of 0.08983(8) days. The superhump amplitude decreased from 0.3 mag at the beginning of the superoutburst to 0.1 mag at its end. In the case of V419 Lyr we have not observed clear secondary humps, which seems to be typical for long period systems.
