No information flow using statistical fluctuations, and quantum cryptography

The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on simple post-selection of suitable experimental runs. The quantum cryptography protocol proposed in the same publication is also examined, and is found to indeed need quantum properties for the system to be secure. However, the security test proposed in the mentioned paper is found to be insufficient, and a modification is proposed here that will ensure security.Comment: revtex4, 9 page

A Kochen-Specker inequality

By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low error rates, in the spirit of the Kochen-Specker theorem. Assuming that the errors are independent, an explicit error bound of 1.42% is derived, below which a Kochen-Specker contradiction occurs.Comment: revtex, 5 pages, 1 figure. v2: journal version (results extended somewhat), epl LaTeX class, 8 pages, 1 figur

Comment on "New Results on Frame-Proof Codes and Traceability Schemes"

In the paper "New Results on Frame-Proof Codes and Traceability Schemes" by Reihaneh Safavi-Naini and Yejing Wang [IEEE Trans. Inform. Theory, vol. 47, no. 7, pp. 3029-3033, Nov. 2001], there are lower bounds for the maximal number of codewords in binary frame-proof codes and decoders in traceability schemes. There are also existence proofs using a construction of binary frame-proof codes and traceability schemes. Here it is found that the main results in the referenced paper do not hold.Comment: 3 page

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

Mubs and Hadamards of Order Six

We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organise our results. Finally we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.Comment: 33 pages, 3 figures. References added in v

Emplacement and 3D geometry of crustal-scale saucer-shaped intrusions in the Fennoscandian Shield

Saucer-shaped intrusions of tens of meters to tens of kilometres across have been observed both from surface geological mapping and geophysical observations. However, there is only one location where they have been reported to extend c. 100 km laterally, and emplaced both in a sedimentary basin and the crystalline basement down to 12 km depth. The legacy BABEL offshore seismic data, acquired over the central Fennoscandian Shield in 1989, have been recovered and reprocessed with the main goal of focusing on this series of globally unique crustal-scale saucer-shaped intrusions present onshore and offshore below the Bothnian Sea. The intrusions (c. 1.25 Ga), emplaced in an extensional setting, are observed within both sedimentary rocks (1.5 Ga). They have oval shapes with diameters ranging 30-100 km. The reprocessed seismic data provide evidence of up-doming of the lower crust (representing the melt reservoir) below the intrusions that, in turn, are observed at different depths in addition to a steep seismically transparent zone interpreted to be a discordant feeder dyke system. Relative age constraints and correlation with onshore saucer-shaped intrusions of different size suggest that they are internally connected and fed by each other from deeper to shallower levels. We argue for a nested emplacement mechanism and against a controlling role by the overlying sedimentary basin as the saucer-shaped intrusions are emplaced in both the sedimentary rocks as well as in the underlying crystalline basement. The interplay between magma pressure and overburden pressure, as well as the, at the time, ambient stress regime, are responsible for their extensive extent and rather constant thicknesses (c. 100-300 m). Saucer-shaped intrusions may therefore be present elsewhere in the crystalline basement to the same extent as observed in this study some of which are a significant source of raw materials.Peer reviewe

Odin observations of H2O in the Galactic Centre

The Odin satellite has been used to detect emission and absorption in the 557-GHz H2O line in the Galactic Centre towards the Sgr A* Circumnuclear Disk (CND), and the Sgr A +20 km/s and +50 km/s molecular clouds. Strong broad H2O emission lines have been detected in all three objects. Narrow H2O absorption lines are present at all three positions and originate along the lines of sight in the 3-kpc Spiral Arm, the -30 km/s Spiral Arm and the Local Sgr Spiral Arm. Broad H2O absorption lines near -130 km/s are also observed, originating in the Expanding Molecular Ring. A new molecular feature (the ``High Positive Velocity Gas'' - HPVG) has been identified in the positive velocity range of ~ +120 to +220 km/s, seen definitely in absorption against the stronger dust continuum emission from the +20 km/s and +50 km/s clouds and possibly in emission towards the position of Sgr A* CND. The 548-GHz H2_18O isotope line towards the CND is not detected at the 0.02 K (rms) level.Comment: 5 pages, 3 figures, accepted by A&A, special Odin Letters issu