Quantum Key Distribution by Utilizing Four-Level Particles

We present a quantum key distribution protocol based on four-level particles entanglement. Furthermore, a controlled quantum key distribution protocol is proposed by utilizing three four-level particles. We show that the two protocols are secure.Comment: 5 pages, no figur

Asteroseismic Study on Cluster Distance Moduli for RGB Stars in NGC 6791 and NGC 6819

Stellar distance is an important basic parameter in stellar astrophysics. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. They are therefore expected to have common properties. These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters, such as stellar mass, metal fraction, and distance when tested against an ensemble of cluster stars. Here we derive a new relation based on solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters $\Delta\nu$ and $\nu_{\rm max}$, and photometric data \textit{V}. The values of $\Delta\nu$ and $\nu_{\rm max}$ are derived from \textit{kepler} observations. At the same time, it is used to interpret the trends between \textit{V} and $\Delta\nu$. From the analyses of this newly derived relation and observational data of NGC 6791 and NGC 6819 we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus. This approach fully reflects the characteristic of member stars in a cluster as a natural sample. From this method we derive true distance moduli of $13.09\pm0.10$ mag for NGC 6791 and $11.88\pm0.14$ mag for NGC 6819. Additionally, we find that the distance modulus only slightly depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in [Fe/H] will lead to a change of 0.06 mag in the distance modulus.Comment: 9 pages, 6 figures, 4 tables, accepted Ap

New asteroseismic scaling relations based on Hayashi track relation applied to red-giant branch stars in NGC 6791 and NGC 6819

Stellar mass $M$, radius $R$, and gravity $g$ are important basic parameters in stellar physics. Accurate values for these parameters can be obtained from the gravitational interaction between stars in multiple systems or from asteroseismology. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. The cluster members are therefore expected to have some properties in common. These common properties strengthen our ability to constrain stellar models and asteroseismically derived $M$, $R$ and $g$ when tested against an ensemble of cluster stars. Here we derive new scaling relations based on a relation for stars on the Hayashi track ($\sqrt{T_{\rm eff}} \sim g^pR^q$) to determine the masses and metallicities of red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global oscillation parameters $\Delta\nu$ (the large frequency separation) and $\nu_{\rm max}$ (frequency of maximum oscillation power). The $\Delta\nu$ and $\nu_{\rm max}$ values are derived from \kepler\ observations. From the analysis of these new relations we derive: (1) direct observational evidence that the masses of red giant branch stars in a cluster are the same within their uncertainties, (2) new methods to derive $M$ and $z$ of the cluster in a self consistent way from $\Delta\nu$ and $\nu_{\rm max}$, with lower intrinsic uncertainties, (3) the mass dependence in the $\Delta\nu$ - $\nu_{\rm max}$ relation for red giant branch stars.Comment: open clusters and associations: individual (NGC 6791, NGC 6819) -- stars: late-type -- stars: fundamental parameters -- stars: interiors -- stars: oscillations -- asteroseismolog