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

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

Minimum detection efficiency for a loophole-free atom-photon Bell experiment

In Bell experiments, one problem is to achieve high enough photodetection to ensure that there is no possibility of describing the results via a local hidden-variable model. Using the Clauser-Horne inequality and a two-photon non-maximally entangled state, a photodetection efficiency higher than 0.67 is necessary. Here we discuss atom-photon Bell experiments. We show that, assuming perfect detection efficiency of the atom, it is possible to perform a loophole-free atom-photon Bell experiment whenever the photodetection efficiency exceeds 0.50.Comment: REVTeX4, 4 pages, 1 figur

Optimal measurement bases for Bell-tests based on the CH-inequality

The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold detection efficiency, and the measurement settings adopted in the test. It is well known that the threshold efficiencies decrease when one considers partially entangled states and that the use of these states, unfortunately, generates a reduction in the CH violation. Nevertheless, these quantities are both dependent on the measurement settings considered, and in this paper we show that there are measurement bases which allow for an optimal situation in this trade-off relation. These bases are given as a generalization of the Hardy measurement bases, and they will be relevant for future Bell tests relying on pairs of entangled qubits.Comment: 8 pages, 6 figure

Qubits from Number States and Bell Inequalities for Number Measurements

Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation, v3: published versio

O18O and C18O observations of rho Oph A

Observations of the (N_J=1_1-1_0) ground state transition of O_2 with the Odin satellite resulted in a about 5 sigma detection toward the dense core rho Oph A. At the frequency of the line, 119 GHz, the Odin telescope has a beam width of 10', larger than the size of the dense core, so that the precise nature of the emitting source and its exact location and extent are unknown. The current investigation is intended to remedy this. Telluric absorption makes ground based O_2 observations essentially impossible and observations had to be done from space. mm-wave telescopes on space platforms were necessarily small, which resulted in large, several arcminutes wide, beam patterns. Although the Earth's atmosphere is entirely opaque to low-lying O_2 transitions, it allows ground based observations of the much rarer O18O in favourable conditions and at much higher angular resolution with larger telescopes. In addition, rho Oph A exhibits both multiple radial velocity systems and considerable velocity gradients. Extensive mapping of the region in the proxy C18O (J=3-2) line can be expected to help identify the O_2 source on the basis of its line shape and Doppler velocity. Line opacities were determined from observations of optically thin 13C18O (J=3-2) at selected positions. During several observing periods, two C18O intensity maxima in rho Oph A were searched for in the 16O18O (2_1-0_1) line at 234 GHz with the 12m APEX telescope. Our observations resulted in an upper limit on the integrated O18O intensity of < 0.01 K km/s (3 sigma) into the 26.5" beam. We conclude that the source of observed O_2 emission is most likely confined to the central regions of the rho Oph A cloud. In this limited area, implied O_2 abundances could thus be higher than previously reported, by up to two orders of magnitude.Comment: 7 pages, 6 figures (5 colour), Astronomy & Astrophysic

Device-independent quantum key distribution secure against collective attacks

Device-independent quantum key distribution (DIQKD) represents a relaxation of the security assumptions made in usual quantum key distribution (QKD). As in usual QKD, the security of DIQKD follows from the laws of quantum physics, but contrary to usual QKD, it does not rely on any assumptions about the internal working of the quantum devices used in the protocol. We present here in detail the security proof for a DIQKD protocol introduced in [Phys. Rev. Lett. 98, 230501 (2008)]. This proof exploits the full structure of quantum theory (as opposed to other proofs that exploit the no-signalling principle only), but only holds again collective attacks, where the eavesdropper is assumed to act on the quantum systems of the honest parties independently and identically at each round of the protocol (although she can act coherently on her systems at any time). The security of any DIQKD protocol necessarily relies on the violation of a Bell inequality. We discuss the issue of loopholes in Bell experiments in this context.Comment: 25 pages, 3 figure