Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

Thermodynamic formalism for dissipative quantum walks

We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.Comment: 8 page

Se-Atom Incorporation in Fullerene and the MD Simulation(II. Radiochemistry)

The formation of Se atom-incorporated fullerenes has been investigated by using radionuclides produced by nuclear reactions. From the trace of radioactivities of ^Se after High Performance Liquid Chromatography (HPLC), it was found that the formation of endohedral fullerenes or heterofullerenes is possible by a recoil process following the nuclear reactions. To confirm the produced materials, ab initio molecular-dynamics simulations based on an all-electron mixed-basis approach were carried out. We found that the insertion of Se atom into C_ cage is much easier than that of As and Ge atoms

Quantification of concurrence via weak measurement

Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely, concurrence, of an arbitrary two-qubit pure state via a single fixed measurement setup by exploiting so-called weak measurements and the associated weak values together with the properties of the Laguerre-Gaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol

Closed timelike curves via post-selection: theory and experimental demonstration

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. CTCs appear in many solutions of Einstein's field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum field theory. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we explore an alternative quantum formulation of CTCs and show that it is physically inequivalent to Deutsch's. Because it is based on combining quantum teleportation with post-selection, the predictions/retrodictions of our theory are experimentally testable: we report the results of an experiment demonstrating our theory's resolution of the well-known `grandfather paradox.Comment: 5 pages, 4 figure

Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases to the critical point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after referee comments, added extra figur

Localization of the Grover walks on spidernets and free Meixner laws

A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.Comment: 32 page

Wnt5a induces ROR1 to associate with 14-3-3ζ for enhanced chemotaxis and proliferation of chronic lymphocytic leukemia cells.

Wnt5a can activate Rho GTPases in chronic lymphocytic leukemia (CLL) cells by inducing the recruitment of ARHGEF2 to ROR1. Mass spectrometry on immune precipitates of Wnt5a-activated ROR1 identified 14-3-3ζ, which was confirmed by co-immunoprecipitation. The capacity of Wnt5a to induce ROR1 to complex with 14-3-3ζ could be blocked in CLL cells by treatment with cirmtuzumab, a humanized mAb targeting ROR1. Silencing 14-3-3ζ via small interfering RNA impaired the capacity of Wnt5a to: (1) induce recruitment of ARHGEF2 to ROR1, (2) enhance in vitro exchange activity of ARHGEF2 and (3) induce activation of RhoA and Rac1 in CLL cells. Furthermore, CRISPR/Cas9 deletion of 14-3-3ζ in ROR1-negative CLL cell-line MEC1, and in MEC1 cells transfected to express ROR1 (MEC1-ROR1), demonstrated that 14-3-3ζ was necessary for the growth/engraftment advantage of MEC1-ROR1 over MEC1 cells. We identified a binding motif (RSPS857SAS) in ROR1 for 14-3-3ζ. Site-directed mutagenesis of ROR1 demonstrated that serine-857 was required for the recruitment of 14-3-3ζ and ARHGEF2 to ROR1, and activation of RhoA and Rac1. Collectively, this study reveals that 14-3-3ζ plays a critical role in Wnt5a/ROR1 signaling, leading to enhanced CLL migration and proliferation

Geometrical aspects of weak measurements and quantum erasers

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.Comment: 11 pages, 4 figure

Transport Properties, Thermodynamic Properties, and Electronic Structure of SrRuO3

SrRuO$_3$ is a metallic ferromagnet. Its electrical resistivity is reported for temperatures up to 1000K; its Hall coefficient for temperatures up to 300K; its specific heat for temperatures up to 230K. The energy bands have been calculated by self-consistent spin-density functional theory, which finds a ferromagnetic ordered moment of 1.45$\mu_{{\rm B}}$ per Ru atom. The measured linear specific heat coefficient $\gamma$ is 30mJ/mole, which exceeds the theoretical value by a factor of 3.7. A transport mean free path at room temperature of $\approx 10 \AA$ is found. The resistivity increases nearly linearly with temperature to 1000K in spite of such a short mean free path that resistivity saturation would be expected. The Hall coefficient is small and positive above the Curie temperature, and exhibits both a low-field and a high-field anomalous behavior below the Curie temperature.Comment: 6 pages (latex) and 6 figures (postscript, uuencoded.) This paper will appear in Phys. Rev. B, Feb. 15, 199