There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given on the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.

Entanglement detection

It may seem inevitable that highly entangled quantum states are susceptible to disturbance through interaction with a decohering environment. However, certain multiqubit entangled states are well protected from common forms of decoherence as the quantum information is hidden in inherently nonlocal degrees of freedom. This review shows that this robustness is enabled by specific measurements on subsets of qubits, implementing a quantum version of an error correction process. Beginning with the basics, the latest understanding of the relation between this form of error correction and the concept of two-dimensional topological order in many-body physics is reviewed.

Quantum error correction for quantum memories

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by graph states, our approach provides a generalization of threshold classical secret sharing via insecure quantum channels beyond the current requirement of 100% collaboration by players to just a simple majority in the case of five players. Another innovation here is the introduction of embedded protocols within a larger graph state that serves as a one-way quantum-information processing system.

Graph states for quantum secret sharing

With the rapid development of quantum technologies, a pressing need has emerged for a wide array of tools for the certification and characterization of quantum devices. Such tools are critical because the powerful applications of quantum information science will only be realized if stringent levels of precision of components can be reached and their functioning guaranteed. This Technical Review provides a brief overview of the known characterization methods for certification, benchmarking and tomographic reconstruction of quantum states and processes, and outlines their applications in quantum computing, simulation and communication. Quantum technologies require an extremely precise functioning of their components which is ensured by sophisticated tools for device characterization. This Technical Review surveys and assesses the currently available tools according to their overall complexity, information gain, and underlying assumptions.

/pdf/quantum-certification-and-benchmarking-33lyv0adbh.pdf

Quantum certification and benchmarking

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.

https://arxiv.org/pdf/quant-ph/0506170.pdf

Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication.

Optimal local discrimination of two multipartite pure states

We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.

Damian Markham

Papers

Graph states for quantum secret sharing

Quantum certification and benchmarking

Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication.

Optimal local discrimination of two multipartite pure states

Quantum secret sharing with qudit graph states