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

Majorization uncertainty relations for mixed quantum states

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of $\rho$ and the entries of a unitary matrix $U$ relating both bases. The obtained results can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as uncertainty relation for the sum of conditional entropies.Comment: 13 pages, 7 figure

Excluding false negative error in certification of quantum channels

Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false negative error after a finite number of queries in parallel, but cannot be distinguished unambiguously. Moreover, it will be proved that parallel certification scheme is always sufficient, however the number of steps may be decreased by the use of adaptive scheme. Finally, we consider examples of certification of various classes of quantum channels and measurements.Comment: 21 pages, 2 figure

The impact of environmental conditions on water salinity in the area of the city of Inowrocław (north-central Poland)

The article presents the influence of natural and anthropogenic factors on the chemical and physical properties of surface and ground waters in the area of the city of Inowrocław. It has been shown that the properties of the waters were most strongly affected by the specific geological structure (the city is located within the Zechstein salt dome) as well as the long-term influence of a salt mine and soda plant. The composition of most analysed samples was dominated by Ca 2+ , Na + and Cl - ions. In places of heavy industrial activity, some water parameters were several time higher than permissible values according to Polish standards. It is concluded that, due to the threat to the city’s ground drinking water resources and fertile soils, the surface and ground waters in the area in question require permanent monitoring

The Effect of Rapid Cooling on the Corrosion Resistance of As-Cast Aluminium Alloy 5052

The effect of rapid cooling by the vacuum suction casting method (VSC) on the microstructure and electrochemical response of the as-cast 5052 aluminium alloy is presented. The VSC method allowed us to obtain massive samples witha very high cooling rate (102 – 103) oC/s. The microstructure of the quick-cooled sample (QC) has been significantly changed. Finer grains and more-homogeneous intermetallic phase distribution has been observed. Corrosion potential (OCP) and polarization measurements (LSV) revealed a higher activity of the QC alloy than ingot (IN), which leads to a denser and thicker corrosion-product formation on the surface. Electrochemical Impedance Spectroscopy (EIS) indicates higher resistance values, which suggests a greater thickness of the corrosion products

Rezensionen

DEUTSCHES POLEN-INSTITUT (ed.) (2006): Frauen. Jahrbuch Polen 2006. Wiesbaden: Harrassowitz. 205 S. BONTER, URSZULA (2005): Der Populärroman in der Nachfolge von E. Marlitt. Wilhelmine Heimburg, Valeska Gräfin Bethusy-Huc, Eufemia von Adlersfeld-Ballestrem. Würzburg: Königshausen & Neumann. 276 S. CORNEJO, RENATA (2006): Das Dilemma des weiblichen Ich. Untersuchungen zur Prosa der 1980er Jahre von Elfriede Jelinek, Anna Mitgutsch und Elisabeth Reichart. Wien: Praesens Verlag. 245 S. ENGEL,MANFRED / LAMPING, DIETER (eds.) (2006): Franz Kafka und die Weltliteratur. Stuttgart: Vandenhoeck & Ruprecht. 378 S. HAAS, AGNIESZKA KATARZYNA (2005): Polskie przekłady Fausta I Goethego. Próba krytyki i zarys recepcji w Polsce. [Polnische Übertragungen von Goethes Faust I. Versuch einer Kritik und eines Überblicks über die Rezeption in Polen]. Gdańsk: Uniwersytet Gdański (=Studia Germanica Gedanensia 12) . 291 S. HARDER, MATTHIAS / HILLE, ALMUT (eds.) (2006): Weltfabrik Berlin. Eine Metropole als Sujet der Literatur. Studien zu Literatur und Landeskunde. Würzburg: Könighausen & Neumann. 306 S. JAROSZEWSKI, MAREK (2006): Życie i twórczość E.T.A. Hoffmanna 1776-1822. [Leben und Werk von E.T.A. Hoffmann 1776-1822]. Gdańsk: WydawnictwoUniwersytetu Gdańskiego. 136 S. SOMMERFELD, BEATE (2007): Kafka-Nachwirkungen in der polnischen Literatur. Unter besonderer Berücksichtigung der achtziger und neunziger Jahre des zwanzigsten Jahrhunderts. Frankfurt (M.)/Berlin/Bern/Bruxelles/New York/Oxford/Wien: Peter Lang Verlag (=Posener Beiträge zur Germanistik 14). 294 S. SUROWSKA, BARBARA L. (2006): Von überspannten Ideen zum politischen Appell. 25 Essays zur deutschen Literatur. Warszawa: Zakład Graficzny Uniwersytetu Warszawskiego. 335 S. EBERT, CHRISTA (2004): Sinaida Hippius. Seltsame Nähe. Ein Porträt. Berlin: Oberbaum Verlag. 393 S. LÖW, ANDREA (2006): Juden im Getto Litzmannstadt. Lebensbedingungen, Selbstwahrnehmung, Verhalten. Göttingen: Wallstein (=Schriftenreihe zur Łódzer [sic!] Getto-Chronik). 584 S. MÄRZ, PETER / VEEN, HANS-JOACHIM (eds.) (2006): Woran erinnern? Der Kommunismus in der deutschen Erinnerungskultur. Köln/Weimar/Wien: Böhlau Verlag. 269 S. MÜNCH, RICHARD (2007): Die akademische Elite. Frankfurt (M.): Suhrkamp. 475 S. ŻYCHLIŃSKI, ARKADIUSZ (2006): Unterwegs zu einem Denker. Eine Studie zur Übersetzbarkeit dichterischer Philosophie am Beispiel der polnischen Übersetzung von Martin Heideggers „Sein und Zeit“. Wrocław/Dresden: Oficyna Wydawnicza ATUT – Wrocławskie Wydawnictwo Oświatowe / Neisse Verlag. 374 S. BREUER, ULRICH / HYVÄRINEN, IRMA (eds.) (2006): Wörter – Verbindungen. Festschrift für Jarmo Korhonen zum 60. Geburtstag. Frankfurt (M.)/Berlin/Bern/Bruxelles/New York/Oxford/Wien: Peter Lang Verlag. 516 S. ŁYP-BIELECKA, ALEKSANDRA (2007): Verben der Nahrungsaufnahme des Deutschen und des Polnischen. Eine semanto-syntaktische Vergleichsanalyse.Frankfurt (M.)/Berlin/Bern/Bruxelles/New York/Oxford/Wien: Peter Lang Verlag (=Danziger Beiträge zur Germanistik 21). 246 S. STEINITZ, KLAUS / KASCHUBA,WOLFGANG (eds.) (2006): Wolfgang Steinitz - Ich hatte unwahrscheinliches Glück. Ein Leben zwischen Wissenschaft und Politik. Berlin: Karl Dietz Verlag. 383 S. ROCHE, JÖRG (2005): Fremdsprachenerwerb – Fremdsprachendidaktik. Tübingen/Basel: A. Francke Verlag. 282 S. ZENDEROWSKA-KORPUS, GRAŻYNA (2004): Sprachliche Schematismen des Deutschen und ihre Vermittlung im Unterricht DaF. Frankfurt (M.)/Berlin/Bern/Bruxelles/New York/Oxford/Wien: Peter Lang Verlag (=Danziger Beiträge zur Germanistik 12). 238 S