Symmetric mixed states of nn qubits: local unitary stabilizers and entanglement classes

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for published versio

Classification of n-qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene

Undetermined states: how to find them and their applications

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.Comment: 6 pages, no figur

Entanglement classes of symmetric Werner states

The symmetric Werner states for $n$ qubits, important in the study of quantum nonlocality and useful for applications in quantum information, have a surprisingly simple and elegant structure in terms of tensor products of Pauli matrices. Further, each of these states forms a unique local unitary equivalence class, that is, no two of these states are interconvertible by local unitary operations.Comment: 4 pages, 1 table, additional references in version 2, revised abstract and introduction in version 3, small clarifications for published version in version

Unintentional high density p-type modulation doping of a GaAs/AlAs core-multi-shell nanowire

Achieving significant doping in GaAs/AlAs core/shell nanowires (NWs) is of considerable technological importance but remains a challenge due to the amphoteric behavior of the dopant atoms. Here we show that placing a narrow GaAs quantum well in the AlAs shell effectively getters residual carbon acceptors leading to an \emph{unintentional} p-type doping. Magneto-optical studies of such a GaAs/AlAs core multi-shell NW reveal quantum confined emission. Theoretical calculations of NW electronic structure confirm quantum confinement of carriers at the core/shell interface due to the presence of ionized carbon acceptors in the 1~nm GaAs layer in the shell. Micro-photoluminescence in high magnetic field shows a clear signature of avoided crossings of the $n=0$ Landau level emission line with the $n=2$ Landau level TO phonon replica. The coupling is caused by the resonant hole-phonon interaction, which points to a large 2D hole density in the structure.Comment: just published in Nano Letters (http://pubs.acs.org/doi/full/10.1021/nl500818k

Search for non-relativistic Magnetic Monopoles with IceCube

The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\,\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\,\mathrm{cm^2}$ to $10^{-21}\,\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of $10^{-22}\,(10^{-24})\,\mathrm{cm^2}$ the flux of non-relativistic GUT monopoles is constrained up to a level of $\Phi_{90} \le 10^{-18}\,(10^{-17})\,\mathrm{cm^{-2}s^{-1}sr^{-1}}$ at a 90% confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure

The IceCube Neutrino Observatory - Contributions to ICRC 2015 Part II: Atmospheric and Astrophysical Diffuse Neutrino Searches of All Flavors

Papers on atmospheric and astrophysical diffuse neutrino searches of all flavors submitted to the 34th International Cosmic Ray Conference (ICRC 2015, The Hague) by the IceCube Collaboration.Comment: 66 pages, 36 figures, Papers submitted to the 34th International Cosmic Ray Conference, The Hague 2015, v2 has a corrected author lis

A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube

Evidence for an extraterrestrial flux of high-energy neutrinos has now been found in multiple searches with the IceCube detector. The first solid evidence was provided by a search for neutrino events with deposited energies $\gtrsim30$ TeV and interaction vertices inside the instrumented volume. Recent analyses suggest that the extraterrestrial flux extends to lower energies and is also visible with throughgoing, $\nu_\mu$-induced tracks from the Northern hemisphere. Here, we combine the results from six different IceCube searches for astrophysical neutrinos in a maximum-likelihood analysis. The combined event sample features high-statistics samples of shower-like and track-like events. The data are fit in up to three observables: energy, zenith angle and event topology. Assuming the astrophysical neutrino flux to be isotropic and to consist of equal flavors at Earth, the all-flavor spectrum with neutrino energies between 25 TeV and 2.8 PeV is well described by an unbroken power law with best-fit spectral index $-2.50\pm0.09$ and a flux at 100 TeV of $\left(6.7_{-1.2}^{+1.1}\right)\cdot10^{-18}\,\mathrm{GeV}^{-1}\mathrm{s}^{-1}\mathrm{sr}^{-1}\mathrm{cm}^{-2}$. Under the same assumptions, an unbroken power law with index $-2$ is disfavored with a significance of 3.8 $\sigma$ ($p=0.0066\%$) with respect to the best fit. This significance is reduced to 2.1 $\sigma$ ($p=1.7\%$) if instead we compare the best fit to a spectrum with index $-2$ that has an exponential cut-off at high energies. Allowing the electron neutrino flux to deviate from the other two flavors, we find a $\nu_e$ fraction of $0.18\pm0.11$ at Earth. The sole production of electron neutrinos, which would be characteristic of neutron-decay dominated sources, is rejected with a significance of 3.6 $\sigma$ ($p=0.014\%$).Comment: 16 pages, 10 figures; accepted for publication in The Astrophysical Journal; updated one referenc