Classification of the Deletion Correcting Capabilities of Reed–Solomon Codes of Dimension Over Prime Fields

Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRSk(l,q,alpha,v), is a code of length l over GF(q) with qk codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are also capable of correcting deletions. We consider a subclass of GRS codes with dimension k=2 and q prime, and study them with respect to deletion correcting capability. We give transformations that either preserve the code or maintain its deletion correction capability. We use this to define equivalent codes; and then use exhaustive and selective computer searches to find inequivalent codes with the highest deletion correcting capabilities. We show that, for the class under consideration, up to l-3 deletions may be corrected. We also show that for lles36 there exist codes with q2 codewords such that receiving only 3 out of t transmitted symbols of a codeword is enough to recover the codeword, thus meeting the bound specified above. We also specify some nice codes which are associated with the smallest field possible for codes of a given length and deletion correcting capability. Some of the identified codes are unique, with respect to the defined equivalence

High-capacity steganography using a shared colour palette

Seppanen, Makela and Keskinarkaus (SMK) have proposed a high-capacity steganographic technique to conceal information within a colour image. The technique is significant because of the high volume of data that is embedded into pixels but it results in a high level of noise and so the quality of the resulting image is not acceptable. A new type of coding structure is proposed, which maintains a high capacity but lowers the level of noise. Secondly, an adaptive algorithm is used to identify pixel values that have a high capacity to distortion ratio. Also the maximum size of the coding structures is limited to improve the capacity/distortion tradeoff. For the tested images, an average capacity of nearly 6 bits/pixel was achieved with a peak signal to noise ratio of 40 dB

Influence of monolayer contamination on electric-field-noise heating in ion traps

Electric field noise is a hinderance to the assembly of large scale quantum computers based on entangled trapped ions. Apart from ubiquitous technical noise sources, experimental studies of trapped ion heating have revealed additional limiting contributions to this noise, originating from atomic processes on the electrode surfaces. In a recent work [A. Safavi-Naini et al., Phys. Rev. A 84, 023412 (2011)] we described a microscopic model for this excess electric field noise, which points a way towards a more systematic understanding of surface adsorbates as progenitors of electric field jitter noise. Here, we address the impact of surface monolayer contamination on adsorbate induced noise processes. By using exact numerical calculations for H and N atomic monolayers on an Au(111) surface representing opposite extremes of physisorption and chemisorption, we show that an additional monolayer can significantly affect the noise power spectrum and either enhance or suppress the resulting heating rates.Comment: 8 pages, 5 figure

Import/Export in Digital Rights Management

The inherently controlled nature of digital rights management systems does little to promote inter-operability of systems provided by different vendors. In this paper, we consider import and export functionality by which multimedia protected by one digital rights management regime can be made available to a multimedia device that supports a different digital rights management regime, without compromising the protection afforded to the content under the original regime. We first identify specific issues to be addressed by developers of digital rights management import/export regimes and outline a variety of methods by which these regimes may be implemented. We then apply our observations to the specific example of import and export of content between the digital rights management regimes defined by the Motion Picture Exports Group and the Open Mobile Alliance

Effect of micromotion and local stress in quantum simulations with trapped ions in optical tweezers

The ability to program and control interactions provides the key to implementing large-scale quantum simulation and computation in trapped ion systems. Adding optical tweezers, which can tune the phonon spectrum and thus modify the phonon-mediated spin-spin interaction, was recently proposed as a way of programming quantum simulators for a broader range of spin models [Arias Espinoza et al., Phys. Rev. A {\bf 103}, 052437]. In this work we study the robustness of our findings in the presence of experimental imperfections: micromotion, local stress, and intensity noise. We show that the effects of micromotion can be easily circumvented when designing and optimizing tweezer patterns to generate a target interaction. Furthermore, while local stress, whereby the tweezers apply small forces on individual ions, may appear to enable further tuning of the spin-spin interactions, any additional flexibility is negligible. We conclude that optical tweezers are a useful method for controlling interactions in trapped ion quantum simulators in the presence of micromotion and imperfections in the tweezer alignment, but require intensity stabilization on the sub-percent level.Comment: 7 pages, 5 figure

Saddle-point scrambling without thermalisation

Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalisation in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator of chaos in quantum systems, despite the fact that saddle points in integrable systems can also drive rapid growth in OTOCs. By analysing the Dicke model and a driven Bose-Hubbard dimer, we demonstrate that the OTOC growth driven by chaos can, nonetheless, be distinguished from that driven by saddle points through the long-term behaviour. Besides quantitative differences in the long-term average, the saddle point gives rise to large oscillations not observed in the chaotic case. The differences are also highlighted by entanglement entropy, which in the chaotic driven dimer matches a Page curve prediction. These results illustrate additional markers that can be used to distinguish chaotic behaviour in quantum systems, beyond the initial exponential growth in OTOCs.Comment: 7 pages, 5 figure

Secure authorization, access control and data integrity in Bluetooth

The Bluetooth standard has a provision for mutual authentication of connecting devices but not their actual users and allows access control during connection setup only. We propose a user authorization and pairing (UAP) application, that has the ability to perform authentication and authorization of users using role based model. The pairing procedure, which exchanges link key between devices, is also performed as a part of the user authorization process. The integrity of the message is guaranteed by using message authentication codes. We also extend an attack on a short PIN during the pairing procedure for devices compliant with the Bluetooth specification version 1.1

Trap-assisted complexes in cold atom-ion collisions

We theoretically investigate the trap-assisted formation of complexes in atom-ion collisions and their impact on the stability of the trapped ion. The time-dependent potential of the Paul trap facilitates the formation of temporary complexes by reducing the energy of the atom, which gets temporarily stuck in the atom-ion potential. As a result, those complexes significantly impact termolecular reactions leading to molecular ion formation via three-body recombination. We find that complex formation is more pronounced in systems with heavy atoms, but the mass has no influence on the lifetime of the transient state. Instead, the complex formation rate strongly depends on the amplitude of the ion's micromotion. We also show that complex formation persists even in the case of a time-independent harmonic trap. In this case, we find higher formation rates and longer lifetimes than the Paul trap, indicating that the atom-ion complex plays an essential role in atom-ion mixtures in optical traps.Comment: 6 pages, 4 figure