Quantum walk as a generalized measuring device

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of particle at position x=i corresponds to a measurement of a POVM element E_i on a qubit. We explicitly construct quantum walks implementing unambiguous state discrimination and SIC-POVM.Comment: 6 pages, 1 figur

Classical and Quantum Fluctuation Theorems for Heat Exchange

The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.Comment: 4 pages, 1 included figure, to appear in Phys Rev Let

Air temperature changes in Toruń (central Poland) from 1871 to 2010

The article presents a detailed analysis of changes in air temperature in Toruń in the period 1871–2010 on the basis of homogenised monthly, seasonal and annual air temperature series which have been newly constructed (i.e. extended by the 50 years of 1871–1920). Over the 140-year study period, a sizeable and statistically significant increase of 0.1 °C per decade was found in the air temperature in Toruń. The greatest increases occurred for spring and winter, at 0.12 and 0.11 °C, respectively. A lesser warming, meanwhile, was recorded for autumn (0.10 °C/10 years), and particularly for summer (0.07 °C/10 years). The air temperature trends are statistically significant for all seasons. Air temperature differences between the monthly averages of three analysed subperiods (1871–1900, 1901–1950 and 1951–2010) and averages for the entire period under review rarely exceeded ± 0.5 °C. In all of these periods, the highest average air temperatures occurred in July and the lowest in January. The period of 1981–2010 had the highest frequency of occurrence of very and extremely warm seasons and years. Meanwhile, the highest frequency of very and extremely cool seasons and years was recorded in the 1940s and in the nineteenth century. In the period of 1871–2010, winters shortened markedly (by 7%) and summers lengthened by 3.8%. All of the presented aspects of air temperature in Toruń, which is representative of the climate of central Poland, are in close agreement with the findings of analogous studies of the same for other areas of Poland and Central Europe

Enhancement and anisotropy of electron Lande factor due to spin-orbit interaction in semiconductor nanowires

We investigate the effective Lande factor in semiconductor nanowires with strong Rashba spin-orbit coupling. Using the $\mathbf{k}\cdot\mathbf{p}$ theory and the envelope function approach we derive a conduction band Hamiltonian where the tensor $g^*$ is explicitly related to the spin-orbit coupling constant $\alpha_R$. Our model includes orbital effects from the Rashba spin-orbit term, leading to a significant enhancement of the effective Lande factor which is naturally anisotropic. For nanowires based on the low-gap, high spin-orbit coupled material InSb, we investigate the anisotropy of the effective Lande factor with respect to the magnetic field direction, exposing a twofold symmetry for the bottom gate architecture. The anisotropy results from the competition between the localization of the envelope function and the spin polarization of the electronic state, both determined by the magnetic field direction.Comment: 12 pages, 12 figure

Morphological discrimination of granular materials by measurement of pixel intensity distribution

The paper provides statistical analysis of the photographs of four various granular materials (peas, pellets, triticale, wood chips). For analysis, the (parametric) ANOVA and the (nonparametric) Kruskal-Wallis tests were applied. Additionally, the (parametric) two-sample t-test and (non-parametric) Wilcoxon Rank-Sum Test for pairwise comparisons were performed. In each case, the Bonferroni correction was used. The analysis shows a statistical evidence of the presence of differences between the respective average discrete pixel intensity distributions (PID), induced by the histograms in each group of photos, which cannot be explained only by the existing differences among single granules of different materials. The proposed approach may contribute to the development of a fast inspection method for comparison and discrimination of granular materials differing from the reference material, in the production process

Limit theorem for a time-dependent coined quantum walk on the line

We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, limit theorems for two special cases are presented

A Mock Data Challenge for the Einstein Gravitational-Wave Telescope

Einstein Telescope (ET) is conceived to be a third generation gravitational-wave observatory. Its amplitude sensitivity would be a factor ten better than advanced LIGO and Virgo and it could also extend the low-frequency sensitivity down to 1--3 Hz, compared to the 10--20 Hz of advanced detectors. Such an observatory will have the potential to observe a variety of different GW sources, including compact binary systems at cosmological distances. ET's expected reach for binary neutron star (BNS) coalescences is out to redshift $z\simeq 2$ and the rate of detectable BNS coalescences could be as high as one every few tens or hundreds of seconds, each lasting up to several days. %in the sensitive frequency band of ET. With such a signal-rich environment, a key question in data analysis is whether overlapping signals can be discriminated. In this paper we simulate the GW signals from a cosmological population of BNS and ask the following questions: Does this population create a confusion background that limits ET's ability to detect foreground sources? How efficient are current algorithms in discriminating overlapping BNS signals? Is it possible to discern the presence of a population of signals in the data by cross-correlating data from different detectors in the ET observatory? We find that algorithms currently used to analyze LIGO and Virgo data are already powerful enough to detect the sources expected in ET, but new algorithms are required to fully exploit ET data.Comment: accepted for publication in Physical Review D -- 18 pages, 8 figure

Consistency of shared reference frames should be reexamined

In a recent Letter [G. Chiribella et al., Phys. Rev. Lett. 98, 120501 (2007)], four protocols were proposed to secretly transmit a reference frame. Here We point out that in these protocols an eavesdropper can change the transmitted reference frame without being detected, which means the consistency of the shared reference frames should be reexamined. The way to check the above consistency is discussed. It is shown that this problem is quite different from that in previous protocols of quantum cryptography.Comment: 3 pages, 1 figure, comments are welcom