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

Annals of physics

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

Quantum theory of open systems

We demonstrate that there exists a universal, near-optimal recovery map—the transpose channel—for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.

/pdf/simple-approach-to-approximate-quantum-error-correction-3cknq598p4.pdf

Simple approach to approximate quantum error correction based on the transpose channel

Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this, we investigate the problem of approximate subsystem codes. Subsystem codes extend the standard formalism of subspace QEC to codes in which only a subsystem within a subspace of states is used to store information in a noise-resilient fashion. Here, we demonstrate easily checkable sufficient conditions for the existence of approximate subsystem codes. Furthermore, for certain classes of subsystem codes and noise processes, we prove the efficacy of the transpose channel as a simple-to-construct recovery map that works nearly as well as the optimal recovery channel. This work generalizes our earlier approach [H. K. Ng and P. Mandayam, Phys. Rev. A 81, 062342 (2010)] of using the transpose channel for the approximate correction of subspace codes to the case of subsystem codes, and brings us closer to a unifying framework for approximate QEC.

Towards a unified framework for approximate quantum error correction

This book is a compilation of notes from a two-week international workshop on the "The Functional Analysis of Quantum Information Theory" that was held at the Institute of Mathematical Sciences during 26/12/2011-06/01/2012. The workshop was devoted to the mathematical framework of quantized functional analysis (QFA), and aimed at illustrating its applications to problems in quantum communication. The lectures were given by Gilles Pisier (Pierre and Marie Curie University and Texas A&M), K.R. Parthasarathy (ISI Delhi), Vern Paulsen (University of Houston), and Andreas Winter (Universitat Autonoma de Barcelona). Topics discussed include Operator Spaces and Completely bounded maps, Schmidt number and Schmidt rank of bipartite entangled states, Operator Systems and Completely Positive Maps, and, Operator Methods in Quantum Information.

The Functional Analysis of Quantum Information Theory

It is demonstrated here that local dynamics have the ability to strongly modify the entangling power of unitary quantum gates acting on a composite system. The scenario is common to numerous physical systems, in which the time evolution involves local operators and nonlocal interactions. To distinguish between distinct classes of gates with zero entangling power we introduce a complementary quantity called gate typicality and study its properties. Analyzing multiple, say $n$, applications of any entangling operator, $U$, interlaced with random local gates we prove that both investigated quantities approach their asymptotic values in a simple exponential form. These values coincide with the averages for random nonlocal operators on the full composite space and could be significantly larger than that of ${U}^{n}$. This rapid convergence to equilibrium, valid for subsystems of arbitrary size, is illustrated by studying multiple actions of diagonal unitary gates and controlled unitary gates.

Impact of local dynamics on entangling power

Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols, they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in dimension d = 2^n, which have particularly beautiful symmetry properties derived from the Clifford algebra. More precisely, we show that there exists a unitary transformation that cyclically permutes such bases. This unitary can be understood as a generalization of the Fourier transform, which exchanges two MUBs, to multiple complementary aspects. We proceed to prove a lower bound for min-entropic entropic uncertainty relations for any set of MUBs and show that symmetry plays a central role in obtaining tight bounds. For example, we obtain for the first time a tight bound for four MUBs in dimension d = 4, which is attained by an eigenstate of our complementarity transform. Finally, we discuss the relation to other symmetries obtained by transformations in discrete phase space and note that the extrema of discrete Wigner functions are directly related to min-entropic uncertainty relations for MUBs.

/pdf/a-transform-of-complementary-aspects-with-applications-to-2qg0vjy6ev.pdf

Prabha Mandayam

Papers

Simple approach to approximate quantum error correction based on the transpose channel

Towards a unified framework for approximate quantum error correction

The Functional Analysis of Quantum Information Theory

Impact of local dynamics on entangling power

A transform of complementary aspects with applications to entropic uncertainty relations