Strategies for optimal single-shot discrimination of quantum measurements

In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product, the program finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.Comment: 13 pages, 4 figure

Vertices cannot be hidden from quantum spatial search for almost all random graphs

In this paper we show that all nodes can be found optimally for almost all random Erd\H{o}s-R\'enyi ${\mathcal G}(n,p)$ graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices, though under different conditions. The first one requires $p=\omega(\log^8(n)/n)$, while the seconds requires $p\geq(1+\varepsilon)\log (n)/n$, where $\varepsilon>0$. The proof was made by analyzing the convergence of eigenvectors corresponding to outlying eigenvalues in the $\|\cdot\|_\infty$ norm. At the same time for $p<(1-\varepsilon)\log(n)/n$, the property does not hold for any matrix, due to the connectivity issues. Hence, our derivation concerning Laplacian matrix is tight.Comment: 18 pages, 3 figur

Does Small Ruminant Lentivirus Infection in Goats Predispose to Bacterial Infection of the Mammary Gland? A Preliminary Study

The aim of this study was to determine whether asymptomatic small ruminant lentivirus seropositive (SRLV-SP) goats were more susceptible to bacterial infection of the udder when lactating by comparing the presence and species of pathogenic bacteria in their milk with the values for seronegative goats (SRLV-SN). Milk samples were collected during morning milking on days 20, 40, 60, 150, and 210 of lactation for three consecutive years and subjected to bacteriological examination. Staphylococcus caprae and S. xylosus were the most frequent strains identified in both SRLV-SP and SRLV-SN goats. The prevalence of pathogenic bacteria was the highest in the 1st lactation, regardless of SRLV status. Moreover, the prevalence of pathogenic bacteria was significantly higher in SRLV-SP goats, but only those in the 5th or further lactation (p = 0.010). This suggests a relationship between long-lasting SRLV infection and susceptibility to bacterial infections of the udder

On the probabilistic quantum error correction

Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the error-correcting procedure for general noise. We generalized the Knill-Laflamme conditions for probabilistically correctable errors. We show that for some noise channels, we should encode the information into a mixed state to maximize the probability of successful error correction. Finally, we investigate an advantage of the probabilistic error-correcting procedure over the deterministic one. Reducing the probability of successful error correction allows for correcting errors generated by a broader class of noise channels. Significantly, if the errors are caused by a unitary interaction with an auxiliary qubit system, we can probabilistically restore a qubit state by using only one additional physical qubit.Comment: 28 pages, 2 figure

Milk Yield and Composition, Technological Properties and Homeostasis Indices at Different Lactation Stages and Parities of Two Polish Dairy Goat Breeds

The purpose of the research was to determine the effect of breed, lactation number, and lactation stage on milk efficiency and goat milk ingredients, these being indicators of milk technological parameters and homeostasis disturbances. Goat breed and number of lactation affected energy-corrected milk, value-corrected milk yield, fat corrected milk, protein, casein, lactose contents and free fatty acids. Additionally, differences in non-fat solids and urea contents were found between two Polish common dairy breeds White Improved (PWI) and Fawn Improved (PFI) goats. Moreover, parity affected milk yield, its acidity and somatic cell count (SCC). Milk yield and milk components were found to vary according to lactation stage. At the beginning of lactation, milk is richer in ingredients which have effect on cheese and yoghurt production. All the goats undergo similar changes related to the lactation stage that is at the same time and this can affect the yield and quality of the curd. In production focused on liquid milk, the age structure of the herd should be properly managed, as the goats in their third lactation or above have higher milk yields, regardless of breed. For cheese production, the PWI breed would be more suitable than PFI as the PWI goat milk contains less SCC and more components essential for milk processing, including caseins