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

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

A new class of superregular matrices and MDP convolutional codes

This paper deals with the problem of constructing superregular matrices that lead to MDP convolutional codes. These matrices are a type of lower block triangular Toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular. We present a new class of matrices that are superregular over a sufficiently large finite field F . Such construction works for any given choice of characteristic of the field F and code parameters ( n , k ,δ) such that ( n − k ) | δ . We also discuss the size of F needed so that the proposed matrices are superregular

Early impact of rotavirus vaccination in a large paediatric hospital in the UK.

The impact of routine rotavirus vaccination on community-acquired (CA) and healthcare-associated (HA) rotavirus gastroenteritis (RVGE) at a large paediatric hospital, UK, was investigated over a 13-year period. A total of 1644 hospitalized children aged 0-15 years tested positive for rotavirus between July 2002 and June 2015. Interrupted time-series analysis demonstrated that, post vaccine introduction (July 2013 to June 2015), CA- and HA-RVGE hospitalizations were 83% [95% confidence interval (CI): 72-90%) and 83% (95% CI: 66-92%] lower than expected, respectively. Rotavirus vaccination has rapidly reduced the hospital rotavirus disease burden among both CA- and HA-RVGE cases

The effect of 12C + 12C rate uncertainties on s-process yields

The slow neutron capture process in massive stars (the weak s-process) produces most of the s-only isotopes in the mass region 60 < A < 90. The nuclear reaction rates used in simulations of this process have a profound effect on the final s-process yields. We generated 1D stellar models of a 25 solar mass star varying the 12C + 12C rate by a factor of 10 and calculated full nucleosynthesis using the post-processing code PPN. Increasing or decreasing the rate by a factor of 10 affects the convective history and nucleosynthesis, and consequently the final yields.Comment: Conference proceedings for the Nuclear Physics in Astrophysics IV conference, 8-12 June 2009. 4 pages, 3 figures. Accepted for publication to the Journal of Physics: Conference Serie

New limits on heavy sterile neutrino mixing in 8B{^{8}\rm{B}}-decay obtained with the Borexino detector

If heavy neutrinos with mass $m_{\nu_{H}}\geq$2$m_e$ are produced in the Sun via the decay ${^8\rm{B}} \rightarrow {^8\rm{Be}} + e^+ + \nu_H$ in a side branch of pp-chain, they would undergo the observable decay into an electron, a positron and a light neutrino $\nu_{H}\rightarrow\nu_{L}+e^++e^-$. In the present work Borexino data are used to set a bound on the existence of such decays. We constrain the mixing of a heavy neutrino with mass 1.5 MeV $\leq m_{\nu_{H}} \le$ 14 MeV to be $|U_{eH}|^2\leq (10^{-3}-4\times10^{-6})$ respectively. These are tighter limits on the mixing parameters than obtained in previous experiments at nuclear reactors and accelerators.Comment: 7 pages, 6 figure

The Main Results of the Borexino Experiment

The main physical results on the registration of solar neutrinos and the search for rare processes obtained by the Borexino collaboration to date are presented.Comment: 8 pages, 8 figgures, To be published as Proceedings of the Third Annual Large Hadron Collider Physics Conference, St. Petersburg, Russia, 201