Multi-Prover Commitments Against Non-Signaling Attacks

We reconsider the concept of multi-prover commitments, as introduced in the late eighties in the seminal work by Ben-Or et al. As was recently shown by Cr\'{e}peau et al., the security of known two-prover commitment schemes not only relies on the explicit assumption that the provers cannot communicate, but also depends on their information processing capabilities. For instance, there exist schemes that are secure against classical provers but insecure if the provers have quantum information processing capabilities, and there are schemes that resist such quantum attacks but become insecure when considering general so-called non-signaling provers, which are restricted solely by the requirement that no communication takes place. This poses the natural question whether there exists a two-prover commitment scheme that is secure under the sole assumption that no communication takes place; no such scheme is known. In this work, we give strong evidence for a negative answer: we show that any single-round two-prover commitment scheme can be broken by a non-signaling attack. Our negative result is as bad as it can get: for any candidate scheme that is (almost) perfectly hiding, there exists a strategy that allows the dishonest provers to open a commitment to an arbitrary bit (almost) as successfully as the honest provers can open an honestly prepared commitment, i.e., with probability (almost) 1 in case of a perfectly sound scheme. In the case of multi-round schemes, our impossibility result is restricted to perfectly hiding schemes. On the positive side, we show that the impossibility result can be circumvented by considering three provers instead: there exists a three-prover commitment scheme that is secure against arbitrary non-signaling attacks

Perturbative analysis of generalized Einstein's theories

The hypothesis that the energy-momentum tensor of ordinary matter is not conserved separately, leads to a non-adiabatic expansion and, in many cases, to an Universe older than usual. This may provide a solution for the entropy and age problems of the Standard Cosmological Model. We consider two different theories of this type, and we perform a perturbative analysis, leading to analytical expressions for the evolution of gravitational waves, rotational modes and density perturbations. One of these theories exhibits satisfactory properties at this level, while the other one should be discarded.Comment: 14 pages, Latex fil

Observational constraints on Rastall's cosmology

Rastall's theory is a modification of General Relativity, based on the non-conservation of the stress-energy tensor. The latter is encoded in a parameter $\gamma$ such that $\gamma = 1$ restores the usual $\nabla_\nu T^{\mu\nu} = 0$ law. We test Rastall's theory in cosmology, on a flat Robertson-Walker metric, investigating a two-fluid model and using the type Ia supernovae Constitution dataset. One of the fluids is pressureless and obeys the usual conservation law, whereas the other is described by an equation of state $p_x = w_x\rho_x$, with $w_x$ constant. The Bayesian analysis of the Constitution set does not strictly constrain the parameter $\gamma$ and prefers values of $w_x$ close to -1. We then address the evolution of small perturbations and show that they are dramatically unstable if $w_x \neq -1$ and $\gamma \neq 1$, i.e. General Relativity is the favored configuration. The only alternative is $w_x = -1$, for which the dynamics becomes independent from $\gamma$.Comment: Latex file, 14 pages, 6 figures in eps format. Substantial modifications performed, main conclusions change

Gravitomagnetism in Metric Theories: Analysis of Earth Satellites Results, and its Coupling with Spin

Employing the PPN formalism the gravitomagnetic field in different metric theories is considered in the analysis of the LAGEOS results. It will be shown that there are several models that predict exactly the same effect that general relativity comprises. In other words, these Earth satellites results can be taken as experimental evidence that the orbital angular momentum of a body does indeed generate space--time geometry, notwithstanding they do not endow general relativity with an outstanding status among metric theories. Additionally the coupling spin--gravitomagnetic field is analyzed with the introduction of the Rabi transitions that this field produces on a quantum system with spin 1/2. Afterwards, a continuous measurement of the energy of this system is introduced, and the consequences upon the corresponding probabilities of the involved gravitomagnetic field will be obtained. Finally, it will be proved that these proposals allows us, not only to confront against future experiments the usual assumption of the coupling spin--gravotimagnetism, but also to measure some PPN parameters and to obtain functional dependences among them.Comment: 10 page

Quantum-classical transition in Scale Relativity

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The Schrodinger and Klein-Gordon equations are demonstrated as geodesic equations in this framework. A development of the intrinsic properties of this theory, using the mathematical tool of Hamilton's bi-quaternions, leads us to a derivation of the Dirac equation within the scale-relativity paradigm. The complex form of the wavefunction in the Schrodinger and Klein-Gordon equations follows from the non-differentiability of the geometry, since it involves a breaking of the invariance under the reflection symmetry on the (proper) time differential element (ds - ds). This mechanism is generalized for obtaining the bi-quaternionic nature of the Dirac spinor by adding a further symmetry breaking due to non-differentiability, namely the differential coordinate reflection symmetry (dx^mu - dx^mu) and by requiring invariance under parity and time inversion. The Pauli equation is recovered as a non-relativistic-motion approximation of the Dirac equation.Comment: 28 pages, no figur

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

Scalar models for the generalized Chaplygin gas and the structure formation constraints

The generalized Chaplygin gas model represents an attempt to unify dark matter and dark energy. It is characterized by a fluid with an equation of state $p = - A/\rho^\alpha$. It can be obtained from a generalization of the DBI action for a scalar, tachyonic field. At background level, this model gives very good results, but it suffers from many drawbacks at perturbative level. We show that, while for background analysis it is possible to consider any value for $\alpha$, the perturbative analysis must be restricted to positive values of $\alpha$. This restriction can be circumvented if the origin of the generalized Chaplygin gas is traced back to a self-interacting scalar field, instead of the DBI action. But, in doing so, the predictions coming from formation of large scale structures reduce the generalized Chaplygin gas model to a kind of quintessence model, and the unification scenario is lost, if the scalar field is the canonical one. However, if the unification condition is imposed from the beginning as a prior, the model may remain competitive. More interesting results, concerning the unification program, are obtained if a non-canonical self-interacting scalar field, inspired by Rastall's theory of gravity, is imposed. In this case, an agreement with the background tests is possible.Comment: Latex file, 25 pages, 33 figures in eps format. New section on scalar models. Accepted for publication in Gravitation&Cosmolog

Interaction of convective organisation with monsoon precipitation, atmosphere, surface and sea: the 2016 INCOMPASS field campaign in India

The INCOMPASS field campaign combines airborne and ground measurements of the 2016 Indian monsoon, towards the ultimate goal of better predicting monsoon rainfall. The monsoon supplies the majority of water in South Asia, but forecasting from days to the season ahead is limited by large, rapidly developing errors in model parametrizations. The lack of detailed observations prevents thorough understanding of the monsoon circulation and its interaction with the land surface: a process governed by boundary‐layer and convective‐cloud dynamics. INCOMPASS used the UK Facility for Airborne Atmospheric Measurements (FAAM) BAe‐146 aircraft for the first project of this scale in India, to accrue almost 100 h of observations in June and July 2016. Flights from Lucknow in the northern plains sampled the dramatic contrast in surface and boundary‐layer structures between dry desert air in the west and the humid environment over the northern Bay of Bengal. These flights were repeated in pre‐monsoon and monsoon conditions. Flights from a second base at Bengaluru in southern India measured atmospheric contrasts from the Arabian Sea, over the Western Ghats mountains, to the rain shadow of southeast India and the south Bay of Bengal. Flight planning was aided by forecasts from bespoke 4 km convection‐permitting limited‐area models at the Met Office and India's NCMRWF. On the ground, INCOMPASS installed eddy‐covariance flux towers on a range of surface types, to provide detailed measurements of surface fluxes and their modulation by diurnal and seasonal cycles. These data will be used to better quantify the impacts of the atmosphere on the land surface, and vice versa. INCOMPASS also installed ground instrumentation supersites at Kanpur and Bhubaneswar. Here we motivate and describe the INCOMPASS field campaign. We use examples from two flights to illustrate contrasts in atmospheric structure, in particular the retreating mid‐level dry intrusion during the monsoon onset

Interaction of convective organisation with monsoon precipitation, atmosphere, surface and sea: the 2016 INCOMPASS field campaign in India

The INCOMPASS field campaign combines airborne and ground measurements of the 2016 Indian monsoon, towards the ultimate goal of better predicting monsoon rainfall. The monsoon supplies the majority of water in South Asia, but forecasting from days to the season ahead is limited by large, rapidly developing errors in model parametrizations. The lack of detailed observations prevents thorough understanding of the monsoon circulation and its interaction with the land surface: a process governed by boundary-layer and convective-cloud dynamics. INCOMPASS used the UK Facility for Airborne Atmospheric Measurements (FAAM) BAe-146 aircraft for the first project of this scale in India, to accrue almost 100 hours of observations in June and July 2016. Flights from Lucknow in the northern plains sampled the dramatic contrast in surface and boundary layer structures between dry desert air in the west and the humid environment over the northern Bay of Bengal. These flights were repeated in pre-monsoon and monsoon conditions. Flights from a second base at Bengaluru in southern India measured atmospheric contrasts from the Arabian Sea, over the Western Ghats mountains, to the rain shadow of southeast India and the south Bay of Bengal. Flight planning was aided by forecasts from bespoke 4km convection-permitting limited-area models at the Met Office and India's NCMRWF. On the ground, INCOMPASS installed eddy-covariance flux towers on a range of surface types, to provide detailed measurements of surface fluxes and their modulation by diurnal and seasonal cycles. These data will be used to better quantify the impacts of the atmosphere on the land surface, and vice versa. INCOMPASS also installed ground instrumentation supersites at Kanpur and Bhubaneswar. Here we motivate and describe the INCOMPASS field campaign. We use examples from two flights to illustrate contrasts in atmospheric structure, in particular the retreating mid-level dry intrusion during the monsoon onset