Classical statistical distributions can violate Bell-type inequalities

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.Comment: v3: Extended version. To be published in J. Phys.

Experimental Falsification of Leggett's Non-Local Variable Model

Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also some models based on non-local variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In this paper, we introduce a family of inequalities, which allow testing Leggett's non-local model versus quantum physics, and which can be tested in an experiment without additional assumptions. Our experimental data falsify Leggett's model and are in agreement with quantum predictions.Comment: 5 pages, 3 figures, 1 tabl

Security and Composability of Randomness Expansion from Bell Inequalities

The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to act as a catalyst, one also speaks of randomness expansion. Colbeck and Kent proposed the first method for generating randomness from untrusted devices, however, without providing a rigorous analysis. This was addressed subsequently by Pironio et al. [Nature 464 (2010)], who aimed at deriving a lower bound on the min-entropy of the data extracted from an untrusted device, based only on the observed non-local behavior of the device. Although that article succeeded in developing important tools towards the acquired goal, it failed in putting the tools together in a rigorous and correct way, and the given formal claim on the guaranteed amount of min-entropy needs to be revisited. In this paper we show how to combine the tools provided by Pironio et al., as to obtain a meaningful and correct lower bound on the min-entropy of the data produced by an untrusted device, based on the observed non-local behavior of the device. Our main result confirms the essence of the improperly formulated claims of Pironio et al., and puts them on solid ground. We also address the question of composability and show that different untrusted devices can be composed in an alternating manner under the assumption that they are not entangled. This enables for superpolynomial randomness expansion based on two untrusted yet unentangled devices.Comment: 12 pages, v3: significant changes: security is proven against adversaries holding only classical side informatio

Irreducible actions and compressible modules

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a critically compressible left $B$-module, then the dimension of its self-injective hull $A$ over the ring of fractions of $A^B$ is bounded by the uniform dimension of $A$ and the number of linear operators generating $B$. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions

Experimental Design for the Gemini Planet Imager

The Gemini Planet Imager (GPI) is a high performance adaptive optics system being designed and built for the Gemini Observatory. GPI is optimized for high contrast imaging, combining precise and accurate wavefront control, diffraction suppression, and a speckle-suppressing science camera with integral field and polarimetry capabilities. The primary science goal for GPI is the direct detection and characterization of young, Jovian-mass exoplanets. For plausible assumptions about the distribution of gas giant properties at large semi-major axes, GPI will be capable of detecting more than 10% of gas giants more massive than 0.5 M_J around stars younger than 100 Myr and nearer than 75 parsecs. For systems younger than 1 Gyr, gas giants more massive than 8 M_J and with semi-major axes greater than 15 AU are detected with completeness greater than 50%. A survey targeting young stars in the solar neighborhood will help determine the formation mechanism of gas giant planets by studying them at ages where planet brightness depends upon formation mechanism. Such a survey will also be sensitive to planets at semi-major axes comparable to the gas giants in our own solar system. In the simple, and idealized, situation in which planets formed by either the "hot-start" model of Burrows et al. (2003) or the core accretion model of Marley et al. (2007), a few tens of detected planets are sufficient to distinguish how planets form.Comment: 15 pages, 9 figures, revised after referee's comments and resubmitted to PAS

Star Formation and the Growth of Stellar Mass

Recent observations have demonstrated a significant growth in the integrated stellar mass of the red sequence since z=1, dominated by a steadily increasing number of galaxies with stellar masses M* < 10^11 M_sun. In this paper, we use the COMBO-17 photometric redshift survey in conjunction with deep Spitzer 24 micron data to explore the relationship between star formation and the growth of stellar mass. We calculate `star formation rate functions' in four different redshift slices, splitting also into contributions from the red sequence and blue cloud for the first time. We find that the growth of stellar mass since z=1 is consistent with the integrated star formation rate. Yet, most of the stars formed are in blue cloud galaxies. If the stellar mass already in, and formed in, z<1 blue cloud galaxies were to stay in the blue cloud the total stellar mass in blue galaxies would be dramatically overproduced. We explore the expected evolution of stellar mass functions, finding that in this picture the number of massive M* > 3x10^10 M_sun blue galaxies would also be overproduced; i.e., most of the new stars formed in blue cloud galaxies are in the massive galaxies. We explore a simple truncation scenario in which these `extra' blue galaxies have their star formation suppressed by an unspecified mechanism or mechanisms; simple cessation of star formation in these extra blue galaxies is approximately sufficient to build up the red sequence at M*<10^11 M_sun.Comment: 9 Pages; ApJ in pres

Analyzing three-player quantum games in an EPR type setup

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

Compatibility and noncontextuality for sequential measurements

A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting "compatibility loophole" and present several methods to rule out certain hidden variable models which obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped ion experiment and apply our analysis to that case.Comment: 15 pages, 2 figures, v2: problem with latex solve

From the Cover: Assignment of an Essential Role for the Neurospora Frequency Gene in Circadian Entrainment to Temperature Cycles

Circadian systems include slave oscillators and central pacemakers, and the cores of eukaryotic circadian clocks described to date are composed of transcription and translation feedback loops (TTFLs). In the model system Neurospora, normal circadian rhythmicity requires a TTFL in which a White Collar complex (WCC) activates expression of the frequency (frq) gene, and the FRQ protein feeds back to attenuate that activation. To further test the centrality of this TTFL to the circadian mechanism in Neurospora, we used low-amplitude temperature cycles to compare WT and frq-null strains under conditions in which a banding rhythm was elicited. WT cultures were entrained to these temperature cycles. Unlike those normal strains, however, frq-null mutants did not truly entrain to the same cycles. Their peaks and troughs always occurred in the cold and warm periods, respectively, strongly suggesting that the rhythm in Neurospora lacking frq function simply is driven by the temperature cycles. Previous reports suggested that a FRQ-less oscillator (FLO) could be entrained to temperature cycles, rather than being driven, and speculated that the FLO was the underlying circadian-rhythm generator. These inferences appear to derive from the use of a phase reference point affected by both the changing waveform and the phase of the oscillation. Examination of several other phase markers as well as results of additional experimental tests indicate that the FLO is, at best, a slave oscillator to the TTFL, which underlies circadian rhythm generation in Neurospora