Estimation of Spin-Spin Interaction by Weak Measurement Scheme

Precisely knowing an interaction Hamiltonian is crucial to realize quantum information tasks, especially to experimentally demonstrate a quantum computer and a quantum memory. We propose a scheme to experimentally evaluate the spin-spin interaction for a two-qubit system by the weak measurement technique initiated by Yakir Aharonov and his colleagues. Furthermore, we numerically confirm our proposed scheme in a specific system of a nitrogen vacancy center in diamond. This means that the weak measurement can also be taken as a concrete example of the quantum process tomography.Comment: 4 pages, 1 table, 2 figures, to appear in Europhysics Letter

Study on Photon Activation Analysis of Carbon in Glasses for Fiber Amplifiers by Using the Flow Method for the Rapid Separation of ^<11>C(II. Radiochemistry)

We have studied nuclear interference from a matrix produced by (γ, n), (γ, 2n), (γ, p) and (n, γ) reactions and a flow method for ^C separation in order to develop an approach for the photon activation analysis of carbon in InF_3-based fluoride, chalcogenide and tellurite glasses for fiber amplifiers. We found that seventeen radionuclides are produced from these glasses and chemical separation is necessary to determine carbon. For the flow method, which involves the fusion of an irradiated sample with an oxidizer, the conversion of ^C into ^CO_2, and the absorption of ^C in ethanolamine solution, we used a mixture of Pb_3O_4 and B_2O_3 as the oxidizer. We also found that the reaction between ^F(γ, n) and ^Na(γ, αn) in the ethanolamine solution produced ^F contamination with fluoride and chalcogenide glasses and that this flow method can only be applied to tellurite glasses. We confirmed that the chemical yield of the flow method was close to 100 % when determining carbon in standard steel samples by using lithium carbonate as a standard sample. We determined that the carbon concentrations in two kinds of tellurite glass were 8 to 13 and 21 to 28 ppm, respectively

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

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

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

Weak Values with Decoherence

The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a general framework of quantum operations to the W operator in parallel with the Kraus representation of the completely positive map for the density operator. The decoherence effect is also investigated in terms of the weak measurement by a shift of a probe wave function of continuous variable. As an application, we demonstrate how the geometric phase is affected by the bit flip noise.Comment: 17 pages, 3 figure

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

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