Conservation laws, uncertainty relations, and quantum limits of measurements

The uncertainty relation between the noise operator and the conserved quantity leads to a bound for the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of ``repeatable'', or ``nondisturbing'', measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound also sets an obstacle to making a small quantum computer.Comment: 4 pages, RevTex, to appear in PR

Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.Comment: 8 pages, REVTEX; typo added, to appear in PR

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page

Measuring processes and the Heisenberg picture

In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is introduced there. Next, we define the concept of system of measurement correlations and that of measuring process. The former is the exact counterpart of instrument in the (generalized) Heisenberg picture. In quantum mechanical systems, we then show a one-to-one correspondence between systems of measurement correlations and measuring processes up to complete equivalence. This is nothing but a unitary dilation theorem of systems of measurement correlations. Furthermore, from the viewpoint of the statistical approach to quantum measurement theory, we focus on the extendability of instruments to systems of measurement correlations. It is shown that all completely positive (CP) instruments are extended into systems of measurement correlations. Lastly, we study the approximate realizability of CP instruments by measuring processes within arbitrarily given error limits.Comment: v

Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed

Establishing Intracranial Brain Tumor Xenografts With Subsequent Analysis of Tumor Growth and Response to Therapy using Bioluminescence Imaging

Transplantation models using human brain tumor cells have served an essential function in neuro-oncology research for many years. In the past, the most commonly used procedure for human tumor xenograft establishment consisted of the collection of cells from culture flasks, followed by the subcutaneous injection of the collected cells in immunocompromised mice. Whereas this approach still sees frequent use in many laboratories, there has been a significant shift in emphasis over the past decade towards orthotopic xenograft establishment, which, in the instance of brain tumors, requires tumor cell injection into appropriate neuroanatomical structures. Because intracranial xenograft establishment eliminates the ability to monitor tumor growth through direct measurement, such as by use of calipers, the shift in emphasis towards orthotopic brain tumor xenograft models has necessitated the utilization of non-invasive imaging for assessing tumor burden in host animals. Of the currently available imaging methods, bioluminescence monitoring is generally considered to offer the best combination of sensitivity, expediency, and cost. Here, we will demonstrate procedures for orthotopic brain tumor establishment, and for monitoring tumor growth and response to treatment when testing experimental therapies

Neutron scattering studies of industry-relevant materials: connecting microscopic behavior to applied properties

Certain systems of oxides, nitrides and carbides have been recognized as the basic components of advanced materials for applications as engineering and electronic ceramics, catalysts, sensors, etc. under extreme environments. An understanding of the basic atomic and electronic properties of these systems will benefit enormously the industrial development, of new materials featuring tailored properties. We present an overview of neutron-scattering studies of the crystal phases, microstructure, phonon and magnetic excitations of key materials including rare-earth phosphates, phosphate glasses, nanostructured metal oxides, as well as silicon nitride and silicon carbide ceramics. A close collaboration among neutron-scattering experimentation, molecular-dynamics simulation and material synthesis is emphasized

Information-Disturbance Tradeoff in Quantum State Discrimination

When discriminating between two pure quantum states, there exists a quantitative tradeoff between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal tradeoff and provide the corresponding quantum measurement. Such an optimal measurement smoothly interpolates between the two limiting cases of maximal information extraction and no measurement at all.Comment: 5 pages, 2 (low-quality) figures. Eq. (20) corrected. Final published versio

Hadron Masses in Medium and Neutron Star Properties

We investigate the properties of the neutron star with relativistic mean field models. We incorporate in the quantum hadrodynamics and in the quark-meson coupling models a possible reduction of meson masses in nuclear matter. The equation of state for neutron star matter is obtained and is employed in Oppenheimer-Volkov equation to extract the maximum mass of the stable neutron star. We find that the equation of state, the composition and the properties of the neutron stars are sensitive to the values of the meson masses in medium.Comment: 18 pages, 5 figures and 2 tables. To be published in EPJ