On Protected Realizations of Quantum Information

There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. One is initialization-based error protection, which involves a quantum operation that is applied before error events occur. The other is operator quantum error correction, which uses a recovery operation applied after the errors. Together, the two approaches make it clear how quantum information can be stored at all stages of a process involving alternating error and quantum operations. In particular, there is always a subsystem that faithfully represents the desired quantum information. We give a definition of faithful realization of quantum information and show that it always involves subsystems. This justifies the "subsystems principle" for realizing quantum information. In the presence of errors, one can make use of noiseless, (initialization) protectable, or error-correcting subsystems. We give an explicit algorithm for finding optimal noiseless subsystems. Finding optimal protectable or error-correcting subsystems is in general difficult. Verifying that a subsystem is error-correcting involves only linear algebra. We discuss the verification problem for protectable subsystems and reduce it to a simpler version of the problem of finding error-detecting codes.Comment: 17 page

Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

On the Invariants of Towers of Function Fields over Finite Fields

We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with the following: What can we say about the invariants of \mathcal{E}; i.e., the asymptotic number of places of degree r for any r\geq 1 in \mathcal{E}, if those of F are known? We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, with at least one positive invariant and certain prescribed invariants being zero. We show the existence of recursive towers attaining the Drinfeld-Vladut bound of order r, for any r\geq 1 with q^r a square. Moreover, we give some examples of recursive towers with all but one invariants equal to zero.Comment: 23 page

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Observation of a 4ΣHe Bound State in the H4e(K−,π−) reaction at 600MeV/c

We have observed a clear peak below the Σ+-production threshold in the 4He(K−,π−) reaction at 600MeV/c and θKπ=4∘. This is confirmation of the existence of the bound state of 4ΣHe, which was reported in the 4He(stoppedK−,π−) reaction. As in the case of stopped kaons, no such peak was found in the 4He(K−,π+) spectrum. Quantitatively reliable parameters for this level have been established. The binding energy and the width of the bound state are 4.4±0.3(stat)±1(syst) MeV and 7.0±0.7(stat)+1.2−0.0(syst) MeV, respectively

Prospect of Studying Hard X- and Gamma-Rays from Type Ia Supernovae

We perform multi-dimensional, time-dependent radiation transfer simulations for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae (SNe Ia). The synthetic spectra and light curves are compared with the sensitivities of current and future observatories for an exposure time of 10^6 seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by SPI on board INTEGRAL places an upper limit for the mass of 56Ni of \lesssim 1.0 Msun, independently from observations in any other wavelengths. Signals from the newly formed radioactive species have not been convincingly measured yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to deepen the observable horizon to provide the high energy emission data for a significant SN Ia sample. We predict that the hard X-ray detectors on board NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach to SNe Ia at \sim15 Mpc, i.e., one SN every few years. Furthermore, according to the present results, the soft gamma-ray detector on board ASTRO-H will be able to detect the 158 keV line emission up to \sim25 Mpc, i.e., a few SNe Ia per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach to SNe Ia at \sim20 - 35 Mpc by MeV observations. Those would provide new diagnostics and strong constraints on explosion models, detecting rather directly the main energy source of supernova light.Comment: 14 pages, 7 figures, 1 table, accepted for publication in Ap

Snowmass CF1 Summary: WIMP Dark Matter Direct Detection

As part of the Snowmass process, the Cosmic Frontier WIMP Direct Detection subgroup (CF1) has drawn on input from the Cosmic Frontier and the broader Particle Physics community to produce this document. The charge to CF1 was (a) to summarize the current status and projected sensitivity of WIMP direct detection experiments worldwide, (b) motivate WIMP dark matter searches over a broad parameter space by examining a spectrum of WIMP models, (c) establish a community consensus on the type of experimental program required to explore that parameter space, and (d) identify the common infrastructure required to practically meet those goals.Comment: Snowmass CF1 Final Summary Report: 47 pages and 28 figures with a 5 page appendix on instrumentation R&

Neutrino masses from new generations

We reconsider the possibility that Majorana masses for the three known neutrinos are generated radiatively by the presence of a fourth generation and one right-handed neutrino with Yukawa couplings and a Majorana mass term. We find that the observed light neutrino mass hierarchy is not compatible with low energy universality bounds in this minimal scenario, but all present data can be accommodated with five generations and two right-handed neutrinos. Within this framework, we explore the parameter space regions which are currently allowed and could lead to observable effects in neutrinoless double beta decay, $\mu - e$ conversion in nuclei and $\mu \rightarrow e \gamma$ experiments. We also discuss the detection prospects at LHC.Comment: 28 pages, 4 figures. Version to be published. Some typos corrected. Improved figures 3 and