Large violation of Bell inequalities with low entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $\frac{\sqrt{n}}{\log n}$ with $n$ inputs, $n$ outputs and $n$-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.Comment: Reference [16] added. Some typos correcte

The development of a natural plankton population in an outdoor tank with nutrient-poor sea water. II. Changes in dissolved carbohydrates and amino acids

terrelations between plankton communities and dissolved carbohydrates and amino acids were investigated under near-natural conditions in sea water enclosed in plastic tanks. In summer 1972 the development of a natural plankton population was followed in a 3-m3 plastic tank for 28 d. In the course of this experiment, concentrations of dissolved neutral carbohydrates and free amino acids were determined. Results are in the range of published data for the open sea with respect to concentrations (0.2-2.5 pnoles dm-3 total sugar; 0.2-3.1 pnoles dm3 total amino acids) and qualitative composition. A plankton succession was observed during the experiment; this was accompanied by distinct alterations in the concentrations of dissolved amino acids and carbohydrates. Glucose and lysine occurred in highest concentrations. Maximum rate of increase was 29 nmoles dm3 h-' for glucose, and 25 nmoles dm3 h-' for lysine. The rates of decrease are in the same range as bacterial uptake rates determined by various authors employing tracer methods. Numerous positive, highly significant correlations suggest heteropoly- saccharides as one source of individual carbohydrates. Relations between certain species within the plankton succession and occurrence of dissolved organic substances were observed. Significant positive correlations existed between glucose and diatoms as well as between glucose, galactose, mannose, arabinose and ribose and phytoplankton biomass. There were also several significant positive correlations of amino acids, especially of valine, leucine and isoleucine with other biological parameters

Hypercontractivity on the qq-Araki-Woods algebras

Extending a work of Carlen and Lieb, Biane has obtained the optimal hypercontractivity of the $q$-Ornstein-Uhlenbeck semigroup on the $q$-deformation of the free group algebra. In this note, we look for an extension of this result to the type III situation, that is for the $q$-Araki-Woods algebras. We show that hypercontractivity from $L^p$ to $L^2$ can occur if and only if the generator of the deformation is bounded.Comment: 17 page

Extended Distal Pancreatectomy with En Bloc Resection of the Celiac Axis for Locally Advanced Pancreatic Cancer: A Case Report and Review of the Literature

Due to a lack of early symptoms, pancreatic cancers of the body and tail are discovered mostly at advanced stages. These locally advanced cancers often involve the celiac axis or the common hepatic artery and are therefore declared unresectable. The extended distal pancreatectomy with en bloc resection of the celiac artery may offer a chance of complete resection. We present the case of a 48-year-old female with pancreatic body cancer invading the celiac axis. The patient underwent laparoscopy to exclude hepatic and peritoneal metastasis. Subsequently, a selective embolization of the common hepatic artery was performed to enlarge arterial flow to the hepatobiliary system and the stomach via the pancreatoduodenal arcades from the superior mesenteric artery. Fifteen days after embolization, the extended distal pancreatectomy with splenectomy and en bloc resection of the celiac axis was carried out. The postoperative course was uneventful, and complete tumor resection was achieved. This case report and a review of the literature show the feasibility and safety of the extended distal pancreatectomy with en bloc resection of the celiac axis. A preoperative embolization of the celiac axis may avoid ischemia-related complications of the stomach or the liver

Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem

Joint system quantum descriptions arising from local quantumness

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely

Motion of rotatory molecular motor and chemical reaction rate

We examine the dependence of the physical quantities of the rotatory molecular motor, such as the rotation velocity and the proton translocation rate, on the chemical reaction rate using the model based only on diffusion process. A peculiar behavior of proton translocation is found and the energy transduction efficiency of the motor protein is enhanced by this behavior. We give a natural explanation that this behavior is universal when certain inequalities between chemical reaction rates hold. That may give a clue to examine whether the motion of the molecular motor is dominated by diffusion process or not.Comment: 12 pages, 8 figure

Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.127

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0