Energy-time entanglement, Elements of Reality, and Local Realism

The Franson interferometer, proposed in 1989 [J. D. Franson, Phys. Rev. Lett. 62:2205-2208 (1989)], beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experiments and Einstein-Podolsky-Rosen (EPR) elements of reality. The mentioned sinusoidal interference pattern is the same as that giving a violation in the usual Bell experiment. Even so, depending on the precise requirements made on the local realist model, this can imply a) no violation, b) smaller violation than usual, or c) full violation of the appropriate statistical bound. Alternatives include a) using only the measurement outcomes as EPR elements of reality, b) using the emission time as EPR element of reality, c) using path realism, or d) using a modified setup. This paper discusses the nature of these alternatives and how to choose between them. The subtleties of this discussion needs to be taken into account when designing and setting up experiments intended to test local realism. Furthermore, these considerations are also important for quantum communication, for example in Bell-inequality-based quantum cryptography, especially when aiming for device independence.Comment: 18 pages, 7 figures, v2 rewritten and extende

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Inequalities for dealing with detector inefficiencies in Greenberger-Horne-Zeilinger-type experiments

In this article we show that the three-particle GHZ theorem can be reformulated in terms of inequalities, allowing imperfect correlations due to detector inefficiencies. We show quantitatively that taking into accout those inefficiencies, the published results of the Innsbruck experiment support the nonexistence of local hidden variables that explain the experimental result.Comment: LaTeX2e, 9 pages, 3 figures, to appear in Phys. Rev. Let

The monomial representations of the Clifford group

We show that the Clifford group - the normaliser of the Weyl-Heisenberg group - can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.Comment: Additional author and exact solutions to the SIC problem in dimension 16 adde

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

The nature of the hard state of Cygnus X-3

The X-ray binary Cygnus X-3 is a highly variable X-ray source that displays a wide range of observed spectral states. One of the main states is significantly harder than the others, peaking at ~ 20 keV, with only a weak low-energy component. Due to the enigmatic nature of this object, hidden inside the strong stellar wind of its Wolf-Rayet companion, it has remained unclear whether this state represents an intrinsic hard state, with truncation of the inner disc, or whether it is just a result of increased local absorption. We study the X-ray light curves from RXTE/ASM and CGRO/BATSE in terms of distributions and correlations of flux and hardness and find several signs of a bimodal behaviour of the accretion flow that are not likely to be the result of increased absorption in a surrounding medium. Using INTEGRAL observations, we model the broad-band spectrum of Cyg X-3 in its apparent hard state. We find that it can be well described by a model of a hard state with a truncated disc, despite the low cut-off energy, if the accreted power is supplied to the electrons in the inner flow in the form of acceleration rather than thermal heating, resulting in a hybrid electron distribution and a spectrum with a significant contribution from non-thermal Comptonization, usually observed only in soft states. The high luminosity of this non-thermal hard state implies that either the transition takes place at significantly higher L/Ledd than in the usual advection models, or the mass of the compact object is > 20 Msun, possibly making it the most massive black hole observed in an X-ray binary in our Galaxy so far. We find that an absorption model as well as a model of almost pure Compton reflection also fit the data well, but both have difficulties explaining other results, in particular the radio/X-ray correlation.Comment: 14 pages, 13 figures, submitted to MNRA

Electromagnetics from a quasistatic perspective

Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however that it is not without confusing issues as has been illustrated by many contributions to this Journal. Quasistatic theory is conceptually useful by providing an intermediate level in between statics and the full set of Maxwell's equations. Quasistatics is easier than general electrodynamics and in some ways more similar to statics. It is however, in terms of interesting physics and important applications, far richer than statics. Quasistatics is much used in electromagnetic modeling, an activity that today is possible on a PC and which also has great pedagogical potential. The use of electromagnetic simulations in teaching gives additional support for the importance of quasistatics. This activity may also motivate some change of focus in the presentation of basic electrodynamics

Necessary and sufficient detection efficiency for the Mermin inequalities

We prove that the threshold detection efficiency for a loophole-free Bell experiment using an $n$-qubit Greenberger-Horne-Zeilinger state and the correlations appearing in the $n$-partite Mermin inequality is $n/(2n-2)$. If the detection efficiency is equal to or lower than this value, there are local hidden variable models that can simulate all the quantum predictions. If the detection efficiency is above this value, there is no local hidden variable model that can simulate all the quantum predictions.Comment: REVTeX4, 5 pages, 1 figur