Generalization of Quantum Error Correction via the Heisenberg Picture

We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may therefore suitably be called ``operator algebra quantum error correction''). In particular, the approach provides a framework for the correction of hybrid quantum-classical information and it does not require the state to be entirely in one of the corresponding subspaces or subsystems. We discuss applications to quantum teleportation and to the study of information flows in quantum interactions.Comment: 5 pages, preprint versio

The Abundance of Kaluza-Klein Dark Matter with Coannihilation

In Universal Extra Dimension models, the lightest Kaluza-Klein (KK) particle is generically the first KK excitation of the photon and can be stable, serving as particle dark matter. We calculate the thermal relic abundance of the KK photon for a general mass spectrum of KK excitations including full coannihilation effects with all (level one) KK excitations. We find that including coannihilation can significantly change the relic abundance when the coannihilating particles are within about 20% of the mass of the KK photon. Matching the relic abundance with cosmological data, we find the mass range of the KK photon is much wider than previously found, up to about 2 TeV if the masses of the strongly interacting level one KK particles are within five percent of the mass of the KK photon. We also find cases where several coannihilation channels compete (constructively and destructively) with one another. The lower bound on the KK photon mass, about 540 GeV when just right-handed KK leptons coannihilate with the KK photon, relaxes upward by several hundred GeV when coannihilation with electroweak KK gauge bosons of the same mass is included.Comment: 38 pages, 4 figure

The Measure of a Measurement

While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is a certain splitting of the total Hilbert space and its recursive iterations to further iterated subdivisions. This paper explores some implications for associated probability measures (in the classical sense of measure theory), specifically their fractal components. We identify a fractal scale $s$ in a family of Borel probability measures $\mu$ on the unit interval which arises independently in quantum information theory and in wavelet analysis. The scales $s$ we find satisfy $s\in \mathbb{R}_{+}$ and $s\not =1$, some $s 1$. We identify these scales $s$ by considering the asymptotic properties of $\mu(J) /| J| ^{s}$ where $J$ are dyadic subintervals, and $| J| \to0$.Comment: 18 pages, 3 figures, and reference

Topological Subsystem Codes

We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational power of code deformation in these codes, and show that boundaries cannot be introduced in the usual way. In addition, we give a general mapping connecting suitable classical statistical mechanical models to optimal error correction in subsystem stabilizer codes that suffer from depolarizing noise.Comment: 16 pages, 11 figures, explanations added, typos correcte

Supersoft Supersymmetry is Super-Safe

We show that supersymmetric models with a large Dirac gluino mass can evade much of the jets plus missing energy searches at LHC. Dirac gaugino masses arise from "supersoft" operators that lead to finite one-loop suppressed contributions to the scalar masses. A little hierarchy between the Dirac gluino mass 5 - 10 times heavier than the squark masses is automatic and technically natural, in stark contrast to supersymmetric models with Majorana gaugino masses. At the LHC, colored sparticle production is suppressed not only by the absence of gluino pair (or associated) production, but also because several of the largest squark pair production channels are suppressed or absent. We recast the null results from the present jets plus missing energy searches at LHC for supersymmetry onto a supersoft supersymmetric simplified model (SSSM). Assuming a massless LSP, we find the strongest bounds are: 748 GeV from a 2j + MET search at ATLAS (4.7 fb^{-1}), and 684 GeV from a combined jets plus missing energy search using $\alpha_T$ at CMS (1.1 fb^{-1}). In the absence of a future observation, we estimate the bounds on the squark masses to improve only modestly with increased luminosity. We also briefly consider the further weakening in the bounds as the LSP mass is increased.Comment: 13 pages, 8 figure