Quantum Logic and the Histories Approach to Quantum Theory

An extended analysis is made of the Gell-Mann and Hartle axioms for a generalised `histories' approach to quantum theory. Emphasis is placed on finding equivalents of the lattice structure that is employed in standard quantum logic. Particular attention is given to `quasi-temporal' theories in which the notion of time-evolution is less rigid than in conventional Hamiltonian physics; theories of this type are expected to arise naturally in the context of quantum gravity and quantum field theory in a curved space-time. The quasi-temporal structure is coded in a partial semi-group of `temporal supports' that underpins the lattice of history propositions. Non-trivial examples include quantum field theory on a non globally-hyperbolic spacetime, and a simple cobordism approach to a theory of quantum topology. It is shown how the set of history propositions in standard quantum theory can be realised in such a way that each history proposition is represented by a genuine projection operator. This provides valuable insight into the possible lattice structure in general history theories, and also provides a number of potential models for theories of this type.Comment: TP/92-93/39 36 pages + one page of diagrams (I could email Apple laser printer postscript file for anyone who is especially keen

Simulating Quantum Mechanics by Non-Contextual Hidden Variables

No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical observables with measurement outcomes that cannot be simulated non-contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that \emph{can} be recovered from a non-contextual hidden variable model. We show here by explicit construction that there are indeed such non-contextual hidden variable models, both for projection valued and positive operator valued measurements.Comment: 15 pages. Journal version. Only minor typo corrections from last versio

Covariant quantum measurements may not be optimal

Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not be a covariant measurement (contrary to widespread belief). It may be advantageous for the receiver to use a different group and an indirect estimation method: first, an ordinary measurement supplies redundant numerical parameters; the latter are then used for a nonlinear optimal identification of the signal.Comment: minor corrections, to appear in J. Mod. Opt. (proc. of Gdansk conf.

Multispectral system analysis through modeling and simulation

The design and development of multispectral remote sensor systems and associated information extraction techniques should be optimized under the physical and economic constraints encountered and yet be effective over a wide range of scene and environmental conditions. Direct measurement of the full range of conditions to be encountered can be difficult, time consuming, and costly. Simulation of multispectral data by modeling scene, atmosphere, sensor, and data classifier characteristics is set forth as a viable alternative, particularly when coupled with limited sets of empirical measurements. A multispectral system modeling capability is described. Use of the model is illustrated for several applications - interpretation of remotely sensed data from agricultural and forest scenes, evaluating atmospheric effects in LANDSAT data, examining system design and operational configuration, and development of information extraction techniques

Atmospheric modeling related to Thematic Mapper scan geometry

A simulation study was carried out to characterize atmospheric effects in LANDSAT-D Thematic Mapper data. In particular, the objective was to determine if any differences would result from using a linear vs. a conical scanning geometry. Insight also was gained about the overall effect of the atmosphere on Thematic Mapper signals, together with the effects of time of day. An added analysis was made of the geometric potential for direct specular reflections (sun glint). The ERIM multispectral system simulation model was used to compute inband Thematic Mapper radiances, taking into account sensor, atmospheric, and surface characteristics. Separate analyses were carried out for the thermal band and seven bands defined in the reflective spectral region. Reflective-region radiances were computed for 40 deg N, 0 deg, and 40 deg S latitudes; June, Mar., and Dec. days; and 9:30 and 11:00 AM solar times for both linear and conical scan modes. Also, accurate simulations of solar and viewing geometries throughout Thematic Mapper orbits were made. It is shown that the atmosphere plays an important role in determining Thematic Mapper radiances, with atmospheric path radiance being the major component of total radiances for short wavelengths and decreasing in importance as wavelength increases. Path radiance is shown to depend heavily on the direct radiation scattering angle and on haze content. Scan-angle-dependent variations were shown to be substantial, especially for the short-wavelength bands

Wheat signature modeling and analysis for improved training statistics: Supplement. Simulated LANDSAT wheat radiances and radiance components

Simulated scanner system data values generated in support of LACIE (Large Area Crop Inventory Experiment) research and development efforts are presented. Synthetic inband (LANDSAT) wheat radiances and radiance components were computed and are presented for various wheat canopy and atmospheric conditions and scanner view geometries. Values include: (1) inband bidirectional reflectances for seven stages of wheat crop growth; (2) inband atmospheric features; and (3) inband radiances corresponding to the various combinations of wheat canopy and atmospheric conditions. Analyses of these data values are presented in the main report

Negativity and contextuality are equivalent notions of nonclassicality

Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.Comment: 5 pages, published version (modulo some supplementary material

Probabilities from envariance?

Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's derivation it is argued that this claim is exaggerated if not wholly unjustified. In order to demonstrate that Born's rule arises noncircularly from deterministically evolving quantum states, it is not sufficient to assume that quantum states are somehow associated with probabilities and then prove that these probabilities are given by Born's rule. One has to show how irreducible probabilities can arise in the context of an ontological no-collapse interpretation of quantum states. It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.Comment: To appear in IJQI; 9 pages, LaTe

A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio