Physical Logic

In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted propositions form a Boolean algebra because they correspond to subsets of an underlying set of spacetime histories. Physical rules of inference, apply not to the propositions in themselves but to the affirmation and denial of these propositions by the actual world. This physical logic may or may not respect the propositions' underlying Boolean structure. We prove that this logic is Boolean if and only if the following three axioms hold: (i) The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied then its negation, or complement, is affirmed. When a physical system is governed by a dynamical law in the form of a quantum measure with the rule that events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid and need to be modified. One promising scheme for quantum mechanics as quantum measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other minor change

Wigner-Yanase skew information as tests for quantum entanglement

A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.Comment: 5 page

Observation of three-photon Greenberger-Horne-Zeilinger entanglement

We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as GHZ states, play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes. Our experimental arrangement is such that we start with two pairs of entangled photons and register one photon in a way that any information as to which pair it belongs to is erased. The registered events at the detectors for the remaining three photons then exhibit the desired GHZ correlations.Comment: Revtex, 4 pages, uses floats, epsfi

Gravitation: Global Formulation and Quantum Effects

A nonintegrable phase-factor global approach to gravitation is developed by using the similarity of teleparallel gravity with electromagnetism. The phase shifts of both the COW and the gravitational Aharonov-Bohm effects are obtained. It is then shown, by considering a simple slit experiment, that in the classical limit the global approach yields the same result as the gravitational Lorentz force equation of teleparallel gravity. It represents, therefore, the quantum mechanical version of the classical description provided by the gravitational Lorentz force equation. As teleparallel gravity can be formulated independently of the equivalence principle, it will consequently require no generalization of this principle at the quantum level.Comment: Latex (IOP style), 14 pages, 3 figures. To appear in Classical and Quantum Gravit

Compositional Heterogeneity of Impact Melt Rocks at the Haughton Impact Structure, Canada: Implications for Planetary Processes and Remote Sensing

Connecting the surface expression of impact crater‐related lithologies to planetary or regional subsurface compositions requires an understanding of material transport during crater formation. Here, we use imaging spectroscopy of six clast‐rich impact melt rock outcrops within the well‐preserved 23.5‐Ma, 23‐km diameter Haughton impact structure, Canada, to determine melt rock composition and spatial heterogeneity. We compare results from outcrop to outcrop, using clasts, groundmass, and integrated clast‐groundmass compositions as tracers of transport during crater‐fill melt rock formation and cooling. Supporting laboratory imaging spectroscopy analyses of 91 melt‐bearing breccia and clast samples and microscopic X‐ray fluorescence elemental mapping of cut samples paired with spectroscopy of identical surfaces validate outcrop‐scale lithological determinations. Results show different clast‐rich impact melt rock compositions at three sites kilometers apart and an inverse correlation between silica‐rich (sandstone, gneiss, and phyllosilicate‐rich shales) and gypsum‐rich rocks that suggests differences in source depth with location. In the target stratigraphy, gypsum is primarily sourced from ~1‐km depth, while gneiss is from >1.8‐km depth, sandstone from >1.3 km, and shales from ~1.6–1.7 km. Observed heterogeneities likely result from different excavation depths coupled with rapid quenching of the melt due to high content of cool clasts. Results provide quantitative constraints for numerical models of impact structure formation and give new details on melt rock heterogeneity important in interpreting mission data and planning sample return of impactites, particularly for bodies with impacts into sedimentary and volatile‐bearing targets, e.g., Mars and Ceres

Bell's theorem without inequalities and without probabilities for two observers

A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of ``nonlocality without inequalities''. However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.Comment: REVTeX, 4 page

Quantum codewords contradict local realism

Quantum codewords are highly entangled combinations of two-state systems. The standard assumptions of local realism lead to logical contradictions similar to those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and Mermin. The new contradictions have some noteworthy features that did not appear in the older ones.Comment: 9 pages LaTeX, 1 figur

Greenberger-Horne-Zeilinger paradox for continuous variables

We show how to construct states for which a Greenberger-Horne-Zeilinger type paradox occurs if each party measures either the position or momentum of his particle. The paradox can be ascribed to the anticommutation of certain translation operators in phase space. We then rephrase the paradox in terms of modular and binary variables. The origin of the paradox is then due to the fact that the associativity of addition of modular variables is true only for c-numbers but does not hold for operators.Comment: 4 pages, no figure

Proposed direct test of a certain type of noncontextuality in quantum mechanics

The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.Comment: 9 pages 2 figure

Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday. Found. Phys. (2009