Generalized Limits for Single-Parameter Quantum Estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.Comment: 4 pages, 1 figure. v2 typos correcte

Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward.Comment: 14 pages, written in memory of Itamar Pitowsk

Optimal control models of the goal-oriented human locomotion

In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We discuss the modeling of both the dynamical system and the cost to be minimized, and we analyze the corresponding optimal synthesis. The main results describe the asymptotic behavior of the optimal trajectories as the target point goes to infinity

Resolving photon number states in a superconducting circuit

Electromagnetic signals are always composed of photons, though in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting qubit to signals on a microwave transmission line, it is possible to construct an integrated circuit where the presence or absence of even a single photon can have a dramatic effect. This system is called circuit quantum electrodynamics (QED) because it is the circuit equivalent of the atom-photon interaction in cavity QED. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit can absorb and re-emit a single photon many times. Here, we report a circuit QED experiment which achieves the strong dispersive limit, a new regime of cavity QED in which a single photon has a large effect on the qubit or atom without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability to find the corresponding photon number in the cavity. This effect has been used to distinguish between coherent and thermal fields and could be used to create a photon statistics analyzer. Since no photons are absorbed by this process, one should be able to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd

Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second versio

Modeling the pharmacodynamics of passive membrane permeability

Small molecule permeability through cellular membranes is critical to a better understanding of pharmacodynamics and the drug discovery endeavor. Such permeability may be estimated as a function of the free energy change of barrier crossing by invoking the barrier domain model, which posits that permeation is limited by passage through a single “barrier domain” and assumes diffusivity differences among compounds of similar structure are negligible. Inspired by the work of Rezai and co-workers (JACS 128:14073–14080, 2006), we estimate this free energy change as the difference in implicit solvation free energies in chloroform and water, but extend their model to include solute conformational affects. Using a set of eleven structurally diverse FDA approved compounds and a set of thirteen congeneric molecules, we show that the solvation free energies are dominated by the global minima, which allows solute conformational distributions to be effectively neglected. For the set of tested compounds, the best correlation with experiment is obtained when the implicit chloroform global minimum is used to evaluate the solvation free energy difference

Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces

Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be partial cases of generic formulas derived by using d^2 x N matrices as a source for constructing arbitrary bases. The known examples of the SIC-POVM, MUBs, and the phase-space description of qubit states are considered from the viewpoint of the developed unified approach. Star-product schemes are classified with respect to associated d^2 x N matrices. In particular, unitary matrices correspond to self-dual schemes. Such self-dual star-product schemes are shown to be determined by dequantizers which do not form POVM.Comment: 12 pages, 1 figure, 1 table, to appear in Journal of Russian Laser Researc

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version <http://www.livingreviews.org/lrr-2009-2

Construction, Concentration, and (Dis)Continuities in Social Valuations

I review and integrate recent sociological research that makes progress on three interrelated questions pertaining to social valuation: (a) the degree of social construction relative to objective constraints; (b) the degree of concentration in social valuations at a single point in time; and (c) the conditions that govern two broad forms of temporal discontinuity—(i) fashion cycles, especially in cultural expression and in managerial practices, and (ii) bubble/crash dynamics, as witnessed in such domains as authoritarian regimes and financial markets. In the course of the review, I argue for the importance of identifying how objective conditions constrain social construction and suggest two contrarian mechanisms by which this is accomplished—valuation opportunism and valuation entrepreneurship—and the conditions under which they are more or less effective

High-growth firms and productivity:evidence from the United Kingdom

Abstract There is considerable evidence that high-growth firms (HGFs) contribute significantly to employment and economic growth. However, the literature so far does not adequately explore the link between HGFs and productivity. This paper investigates the empirical link between total factor productivity (TFP) growth and HGFs, defined in terms of sales growth, in the United Kingdom over the period 2001-2010, by examining two related research questions. Firstly, does higher TFP growth lead to HGF status and secondly, does HGF experience help firms achieve faster TFP growth? Our findings reveal that firms in both the manufacturing and services sectors are more likely to become HGFs when they exhibit higher TFP growth. In addition, firms that have had HGF experience tend to enjoy faster TFP growth following the high-growth episodes. Policy implications are drawn based on the self-reinforcing process of the high-growth phenomenon that is revealed by our results