The Finite Basis Problem for Kiselman Monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke--Kiselman monoids including the Kiselman monoids $\mathcal{K}_n$. As a consequence, we conclude that the identities of $\mathcal{K}_n$ are nonfinitely based for every $n\ge 4$ and exhibit a finite identity basis for the identities of each of the monoids $\mathcal{K}_2$ and $\mathcal{K}_3$. In the third version a question left open in the initial submission has beed answered.Comment: 16 pages, 1 table, 1 figur

Lower bound for the quantum capacity of a discrete memoryless quantum channel

We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof is restricted to the binary quantum channels, but its extension of to l-adic channels is straightforward.Comment: 16 pages, REVTeX4. To appear in J. Math. Phys. A critical error in fidelity calculation was corrected by using Hamada's result (quant-ph/0112103). In the third version, we simplified formula and derivation of the lower bound by proving p(Gamma)+q(Gamma)=1. In the second version, we added an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer code

How to correct small quantum errors

The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a non-vanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T, provided the errors produced by T are small enough.Comment: LaTeX2e, 23 pages, 6 figures (3 eps, 3 pstricks

Directional Sensitivity of the NEWSdm Experiment to Cosmic Ray Boosted Dark Matter

We present a study of a directional search for Dark Matter boosted forward when scattered by cosmic-ray nuclei, using a module of the NEWSdm experiment. The boosted Dark Matter flux at the edge of the Earth's atmosphere is expected to be pointing to the Galactic Center, with a flux 15 to 20 times larger than in the transverse direction. The module of the NEWSdm experiment consists of a 10 kg stack of Nano Imaging Trackers, i.e.~newly developed nuclear emulsions with AgBr crystal sizes down to a few tens of nanometers. The module is installed on an equatorial telescope. The relatively long recoil tracks induced by boosted Dark Matter, combined with the nanometric granularity of the emulsion, result in an extremely low background. This makes an installation at the INFN Gran Sasso laboratory, both on the surface and underground, viable. A comparison between the two locations is made. The angular distribution of nuclear recoils induced by boosted Dark Matter in the emulsion films at the surface laboratory is expected to show an excess with a factor of 3.5 in the direction of the Galactic Center. This excess allows for a Dark Matter search with directional sensitivity. The surface laboratory configuration prevents the deterioration of the signal in the rock overburden and it emerges as the most powerful approach for a directional observation of boosted Dark Matter with high sensitivity. We show that, with this approach, a 10 kg module of the NEWSdm experiment exposed for one year at the Gran Sasso surface laboratory can probe Dark Matter masses between 1 keV/c$^2$ and 1 GeV/c$^2$ and cross-section values down to $10^{-30}$~cm$^2$ with a directional sensitive search.Comment: 15 pages, 14 figures, updated references, clarified discussion in intro section. Submitted to JCA

NEWSdm Collaboration

Direct Dark Matter searches are nowadays one of the most fervid research topics with many experimental efforts devoted to the search for nuclear recoils induced by the scattering of Weakly Interactive Massive Particles (WIMPs). Detectors able to reconstruct the direction of the nucleus recoiling against the scattering WIMP are opening a new frontier to possibly extend Dark Matter searches beyond the neutrino background. Exploiting directionality would also prove the galactic origin of Dark Matter with an unambiguous signal-to-background separation. Indeed, the angular distribution of recoiled nuclei is centered around the direction of the Cygnus constellation, while the background distribution is expected to be isotropic. Current directional experiments are based on gas TPC whose sensitivity is limited by the small achievable detector mass. In this paper we present the discovery potential of a directional experiment based on the use of a solid target made of newly developed nuclear emulsions and of optical read-out systems reaching unprecedented nanometric resolution

Determination of a time-shift in the OPERA set-up using high energy horizontal muons in the LVD and OPERA detectors

The purpose of this work is to report the measurement of a time-shift in the OPERA set-up in a totally independent way from Time Of Flight (TOF) measurements of CNGS neutrino events. The LVD and OPERA experiments are both installed in the same laboratory: LNGS. The relative position of the two detectors, separated by an average distance of ~ 160 m, allows the use of very high energy horizontal muons to cross-calibrate the timing systems of the two detectors, using a TOF technique which is totally independent from TOF of CNGS neutrino events. Indeed, the OPERA-LVD direction lies along the so-called "Teramo anomaly", a region in the Gran Sasso massif where LVD has established, many years ago, the existence of an anomaly in the mountain structure, which exhibits a low m. w. e. thickness for horizontal directions. The "abundant" high-energy horizontal muons (nearly 100 per year) going through LVD and OPERA exist because of this anomaly in the mountain orography. The total live time of the data in coincidence correspond to 1200 days from mid 2007 until March 2012. The time coincidence study of LVD and OPERA detectors is based on 306 cosmic horizontal muon events and shows the existence of a negative time shift in the OPERA set-up of the order of deltaT(AB) = - (73 \pm 9) ns when two calendar periods, A and B, are compared. This result shows a systematic effect in the OPERA timing system from August 2008 until December 2011. The size of the effect is comparable with the neutrino velocity excess recently measured by OPERA. It is probably interesting not to forget that with the MRPC technology developed by the ALICE Bologna group the TOF world record accuracy of 20 ps was reached. That technology can be implemented at LNGS for a high precision determination of TOF with the CNGS neutrino beams of an order of magnitude smaller than the value of the OPERA systematic effect