Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Simultaneous histories, path sums, and measurements for noncommuting variables

We analyze von Neumann-like quantum measurements in terms of simultaneous virtual paths constructed for two noncommuting variables. The approach is applied to measurements of operator functions of conjugate variables and to the joint measurements of such variables. The limits of applicability of the restricted phase space path integral are studied. We demonstrate that, for a simple joint measurement, using entangled meter states allows one to manipulate the order in which the measurements are conducted. The effects of '' weakening '' a measurement by choosing unsharp meter states are also discussed.

Nature of quantum measurement for quantities not represented by Hermitian operators

In the case of a simple quantum system, we investigate the possibility of defining meaningful probabilities for a quantity that cannot be represented by a Hermitian operator. We find that the consistent-histories approach, recently applied to the case of quantum traversal time [N. Yamada, Phys. Rev. Lett. 83, 3350 (1999)], does not provide a suitable criterion and we dispute Yamada's claim of finding a simple solution to the tunneling-time problem. Rather, we define the probabilities for certain types of generally nonorthogonal decomposition of the system's quantum state. These relate to the interaction between the system and its environment, can be observed in a generalized von Neumann measurement, and are consistent with a particular class of positive-operator-valued measures.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Discovery of novel Agonists and antagonists of the free fatty acid receptor 1 (FFAR1) using virtual screening

The G-protein-coupled receptor free fatty acid receptor 1 (FFAR1), previously named GPR40, is a possible novel target for the treatment of type 2 diabetes. In an attempt to identify new ligands for this receptor, we performed virtual screening (VS) based on two-dimensional (2D) similarity, three-dimensional (3D) pharmacophore searches, and docking studies by using the structure of known agonists and our model of the ligand binding site, which was validated by mutagenesis. VS of a database of 2.6 million compounds followed by extraction of structural neighbors of functionally confirmed hits resulted in identification of 15 compounds active at FFAR1 either as full agonists, partial agonists, or pure antagonists. Site-directed mutagenesis and docking studies revealed different patterns of ligand-receptor interactions and provided important information on the role of specific amino acids in binding and activation of FFAR1.

Identification of residues important for agonist recognition and activation in GPR40

GPR40 was formerly an orphan G protein-coupled receptor whose endogenous ligands have recently been identified as free fatty acids (FFAs). The receptor, now named FFA receptor 1, has been implicated in the pathophysiology of type 2 diabetes and is a drug target because of its role in FFA-mediated enhancement of glucose-stimulated insulin release. Guided by molecular modeling, we investigated the molecular determinants contributing to binding of linoleic acid, a C18 polyunsaturated FFA, and GW9508, a synthetic small molecule agonist. Twelve residues within the putative GPR40-binding pocket including hydrophilic/positively charged, aromatic, and hydrophobic residues were identified and were subjected to site-directed mutagenesis. Our results suggest that linoleic acid and GW9508 are anchored on their carboxylate groups by Arg183, Asn244, and Arg258. Moreover, His86, Tyr91, and His137 may contribute to aromatic and/or hydrophobic interactions with GW9508 that are not present, or relatively weak, with linoleic acid. The anchor residues, as well as the residues Tyr12, Tyr91, His137, and Leu186, appear to be important for receptor activation also. Interestingly, His137 and particularly His86 may interact with GW9508 in a manner dependent on its protonation status. The greater number of putative interactions between GPR40 and GW9508 compared with linoleic acid may explain the higher potency of GW9508.

Increasing entanglement through engineered disorder in the random Ising chain

The ground-state entanglement entropy between block of sites in the random Ising chain is studied by means of the Von Neumann entropy. We show that in presence of strong correlations between the disordered couplings and local magnetic fields the entanglement increases and becomes larger than in the ordered case. The different behavior with respect to the uncorrelated disordered model is due to the drastic change of the ground state properties. The same result holds also for the random three-state quantum Potts model.

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states

The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here, we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation with discord, and characterize the maximally quantum-correlated mixed states, that simultaneously extremize both quantifiers at given von Neumann entropy: among all two-qubit states, these states possess the most robust quantum correlations against noise.

Extremal quantum correlations: Experimental study with two-qubit states

We explore experimentally the space of two-qubit quantum-correlated mixed states, including frontier states as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations.