Quantum Information Geometry in the Space of Measurements

We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can enhance quantum key distribution (QKD). Each network we examine is an n-photon quantum state with a degree of entanglement. We analyze such a state within the space of measured data from repeated experiments made by n observers over a set of identically-prepared quantum states -- a quantum state interrogation in the space of measurements. Each observer records a 1 if their detector triggers, otherwise they record a 0. This generates a string of 1's and 0's at each detector, and each observer can define a binary random variable from this sequence. We use a well-known information geometry-based measure of distance that applies to these binary strings of measurement outcomes, and we introduce a generalization of this length to area, volume and higher-dimensional volumes. These geometric equations are defined using the familiar Shannon expression for joint and mutual entropy. We apply our approach to three distinct tripartite quantum states: the GHZ state, the W state, and a separable state P. We generalize a well-known information geometry analysis of a bipartite state to a tripartite state. This approach provides a novel way to characterize quantum states, and it may have favorable scaling with increased number of photons.Comment: 21 pages, 7 figure

Squeezing more out of a laser

A laser's intensity can be stabilized by negative feedback from a conventional photodetector. I propose extraction of sub-shot-noise light from the feedback loop at a beam splitter by illuminating the back side of the beam splitter with squeezed-state light

Predicting Future Duration from Present Age: A Critical Assessment

Using a temporal version of the Copernican principle, Gott has proposed a statistical predictor of future longevity based on present age [J. R. Gott III, Nature 363, 315 (1993)] and applied the predictor to a variety of examples, including the longevity of the human species. Though Gott's proposal contains a grain of truth, it does not have the universal predictive power that he attributes to it.Comment: 17 pages, standard LaTeX; to be published in Contemporary Physic

Properties of the frequency operator do not imply the quantum probability postulate

We review the properties of the frequency operator for an infinite number of systems and disprove claims in the literature that the quantum probability postulate can be derived from these properties.Comment: 21 pages, no figures, REVTEX. Only change in v.2 is change the title of Sec. IIIC so that it doesn't have a \cite command in it. v.3 incorporates changes that will be published as an erratum in Annals of Physic

Effects of mergers and acquisitions on the economy: an industrial organization perspective

Consolidation and merger of corporations ; Industries

Particle-Number-Conserving Bogoliubov Approximation for Bose-Einstein Condensates Using Extended Catalytic States

We encode the many-body wavefunction of a Bose-Einstein condensate (BEC) in the $N$-particle sector of an extended catalytic state. This catalytic state is a coherent state for the condensate mode and an arbitrary state for the modes orthogonal to the condensate mode. Going to a time-dependent interaction picture where the state of the condensate mode is displaced to the vacuum, we can organize the effective Hamiltonian by powers of ${N}^{-1/2}$. Requiring the terms of order ${N}^{1/2}$ to vanish gives the Gross-Pitaevskii equation. Going to the next order, $N^0$, we derive equations for the number-conserving Bogoliubov approximation, first given by Castin and Dum [Phys. Rev. A $\textbf{57}$, 3008 (1998)]. In contrast to other approaches, ours is well suited to calculating the state evolution in the Schr\"{o}dinger picture; moreover, it is straightforward to generalize our method to multi-component BECs and to higher-order corrections.Comment: 29 pages, 1 figur

Gravitational radiation and the ultimate speed in Rosen's Bimetric theory of gravity

Emission of gravitational radiation was shown to prevent particles of nonzero rest mass from exceeding the speed of gravitational radiation

Explicit product ensembles for separable quantum states

We present a general method for constructing pure-product-state representations for density operators of $N$ quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the density operator. We derive the condition for separability of a mixture of the Greenberger-Horne-Zeilinger state with the maximally mixed state.Comment: 15 pages, no figure