A class of genuinely high-dimensionally entangled states with a positive partial transpose

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled from them. On the other hand, it has been shown recently that some of these PPT states exhibit genuinely high-dimensional entanglement, i.e. they have a high Schmidt number. Here we investigate $d\times d$ dimensional PPT states for $d\ge 4$ discussed recently by Sindici and Piani, and by generalizing their methods to the calculation of Schmidt numbers we show that a linear $d/2$ scaling of its Schmidt number in the local dimension $d$ can be attained.Comment: 8 page

Civil ideals, human rights and social change of the East European post-socialism

Der Autor greift bei seinen Reflexionen über das moderne politische Denken in Osteuropa auf die Theorie der multikulturellen Staatsbürgerschaft von Will Kymlicka (1995) und die Theorie der Anerkennung von Charles Taylor (1992) zurück. Um eine Alternative zu diesen liberalen multikulturellen Deutungen von Kultur aufzuzeigen, betrachtet er den Transformationsprozess in Osteuropa aus der Perspektive einer kritischen Anthropologie und interpretiert das Kulturelle weniger als Bestandteil einer "bürgerlichen Politik", sondern eher als umstrittenen und offenen Prozess. Denn diese analytische Wende bietet die Möglichkeit, unterschiedliche Identitäten und gesellschaftliche Arrangements von Macht in den Blick zu nehmen. Die Bedeutung des Kulturellen in der postsozialistischen Zivilgesellschaft kann nach der These des Autors nur jenseits eines liberalen Multikulturalismus verstanden werden, da die Herausbildung von kulturellen Identitäten und Beziehungen in den Kontext der Macht gestellt werden muss. Er diskutiert vor diesem Hintergrund die Funktion von Identitätspolitiken in Osteuropa sowie die konfliktreiche Beziehung von Minderheiten und neuen Identitäten zwischen Menschenrechten und sozialem Wandel. (ICI

Followers or activists? Social scientists in the reality shows of transformation

Institution building in the knowledge sector; Re-institutionalization of scientific schools; Experts and advisors; Think tanks and transformation; Social criticism and the new elite; Have scholars taken part in local democratic transitions? Historians and/or judges - are these alternative role sets for social researchers during the transformation decade? Policy impacts in theory building

Needed but Rejected: How to Implement the Financial Stability Objective into Monetary Policy?

The 2008 crisis forced central bankers and the representatives of academic literature to reassess the prevailing consensus on practice of monetary policy. Among other topics, the spotlight also fell on the question that how financial stability must be treated. Debate renewed on whether the central bank must play an active role in preventing and managing market turmoil, which consists of leaning against the wind of markets. This paper summarises opinions on this issue and offers our own conclusions. We found that currently neither the theoretical background nor empirical experience provide compelling evidence or a reference for central bankers to move away from their existing monetary policy framework and adopt a leaning against the wind policy. We conclude that the direct integration of financial stability considerations into monetary policy decision-making - i.e. as a form of rules - is not expected in the near future. However, we think that the debate remains open for two reasons: firstly, there is some uncertainty regarding the success of macroprudential regulation and its proper cooperation with monetary policy and secondly, the theoretical development of the implementation of financial cycles into monetary decision-making may also yield results

Surjective Lévy-Prokhorov Isometries

According to the fundamental work of Yu.V. Prokhorov, the general theory of stochastic processes can be regarded as the theory of probability measures in complete separable metric spaces. Since stochastic processes depending upon a continuous parameter are basically probability measures on certain subspaces of the space of all functions of a real variable, a particularly important case of this theory is when the underlying metric space has a linear structure. Prokhorov also provided a concrete metrisation of the topology of weak convergence today known as the L\'evy-Prokhorov distance. Motivated by these facts and some recent works related to the characterisation of onto isometries of spaces of Borel probability measures, here we give the complete description of the structure of surjective L\'evy-Prokhorov isometries on the space of all Borel probability measures on an arbitrary separable real Banach space. Our result can be considered as a generalisation of L. Moln\'ar's earlier result which characterises surjective L\'evy isometries of the space of all probability distribution functions on the real line. However, the present more general setting requires the development of an essentially new technique

Platonic Bell inequalities for all dimensions

In this paper we study the Platonic Bell inequalities for all possible dimensions. There are five Platonic solids in three dimensions, but there are also solids with Platonic properties (also known as regular polyhedra) in four and higher dimensions. The concept of Platonic Bell inequalities in the three-dimensional Euclidean space was introduced by Tavakoli and Gisin [Quantum 4, 293 (2020)]. For any three-dimensional Platonic solid, an arrangement of projective measurements is associated where the measurement directions point toward the vertices of the solids. For the higher dimensional regular polyhedra, we use the correspondence of the vertices to the measurements in the abstract Tsirelson space. We give a remarkably simple formula for the quantum violation of all the Platonic Bell inequalities, which we prove to attain the maximum possible quantum violation of the Bell inequalities, i.e. the Tsirelson bound. To construct Bell inequalities with a large number of settings, it is crucial to compute the local bound efficiently. In general, the computation time required to compute the local bound grows exponentially with the number of measurement settings. We find a method to compute the local bound exactly for any bipartite two-outcome Bell inequality, where the dependence becomes polynomial whose degree is the rank of the Bell matrix. To show that this algorithm can be used in practice, we compute the local bound of a 300-setting Platonic Bell inequality based on the halved dodecaplex. In addition, we use a diagonal modification of the original Platonic Bell matrix to increase the ratio of quantum to local bound. In this way, we obtain a four-dimensional 60-setting Platonic Bell inequality based on the halved tetraplex for which the quantum violation exceeds the $\sqrt 2$ ratio.Comment: 24 pages, 2 figures, 3 tables. Accepted for publication in Quantu