Efficient entanglement distillation without quantum memory

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.

Singlet extensions of the standard model at LHC Run 2: benchmarks and comparison with the NMSSM

The Complex singlet extension of the Standard Model (CxSM) is the simplest extension that provides scenarios for Higgs pair production with different masses. The model has two interesting phases: the dark matter phase, with a Standard Model-like Higgs boson, a new scalar and a dark matter candidate; and the broken phase, with all three neutral scalars mixing. In the latter phase Higgs decays into a pair of two different Higgs bosons are possible. In this study we analyse Higgs-to-Higgs decays in the framework of singlet extensions of the Standard Model (SM), with focus on the CxSM. After demonstrating that scenarios with large rates for such chain decays are possible we perform a comparison between the NMSSM and the CxSM. We find that, based on Higgs-to-Higgs decays, the only possibility to distinguish the two models at the LHC run 2 is through final states with two different scalars. This conclusion builds a strong case for searches for final states with two different scalars at the LHC run 2. Finally, we propose a set of benchmark points for the real and complex singlet extensions to be tested at the LHC run 2. They have been chosen such that the discovery prospects of the involved scalars are maximised and they fulfil the dark matter constraints. Furthermore, for some of the points the theory is stable up to high energy scales. For the computation of the decay widths and branching ratios we developed the Fortran code sHDECAY, which is based on the implementation of the real and complex singlet extensions of the SM in HDECAY.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Using the Higgs to Probe Naturalness

The extreme sensitivity of the mass of the Higgs boson to quantum corrections from high mass states, makes it 'unnaturally' light in the standard model. This 'hierarchy problem' can be solved by symmetries, which predict new particles related, by the symmetry, to standard model fields. The Large Hadron Collider (LHC) can potentially discover these new particles, thereby finding the solution to the hierarchy problem. However, the dynamics of the Higgs boson is also sensitive to this new physics. We show that in many scenarios the Higgs can be a complementary and powerful probe of the hierarchy problem at the LHC and future colliders. If the top quark partners carry the color charge of the strong nuclear force, the production of Higgs pairs is affected. This effect is tightly correlated with single Higgs production, implying that only modest enhancements in di-Higgs production occur when the top partners are heavy. However, if the top partners are light, we show that di-Higgs production is a useful complementary probe to single Higgs production. We verify this result in the context of a simplified supersymmetric model. If the top partners do not carry color charge, their direct production is greatly reduced. Nevertheless, we show that such scenarios can be revealed through Higgs dynamics. We find that many color neutral frameworks leave observable traces in Higgs couplings, which, in some cases, may be the only way to probe these theories at the LHC. Some realizations of the color neutral framework also lead to exotic decays of the Higgs with displaced vertices. We show that these decays are so striking that the projected sensitivity for these searches, at hadron colliders, is comparable to that of searches for colored top partners. Taken together, these three case studies show the efficacy of the Higgs as a probe of naturalness.

Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.