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

All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Quantum networks provide opportunities and challenges across a range of intellectual and technical frontiers, including quantum computation, communication and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for generating and characterizing quantum coherence and entanglement. Fundamental to this endeavour are quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner. Such quantum connectivity in networks can be achieved by the optical interactions of single photons and atoms, allowing the distribution of entanglement across the network and the teleportation of quantum states between nodes.

The quantum internet

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

/pdf/supplementary-information-for-quantum-supremacy-using-a-3tkhfafpzk.pdf

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

We present a broad investigation of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel multiple times and observing its output at the end. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and non-adaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. Our main result is the first separation between adaptive and non-adaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for non-adaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. Full details in [1].

Asymptotic Separation Between Adaptive and Non-adaptive Strategies in Quantum Channel Discrimination

A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain replication lemma for unitaries.

Infinite-Dimensional Programmable Quantum Processors

A tridentate bis-NHC Pd complex, based on caffeine, was studied for its catalytic activity. This complex displayed a high catalytic activity in the Suzuki–Miyaura and Mizoroki–Heck cross-coupling reactions of aryl halides. The Sonogashira cross-coupling was also investigated but reveals a fast plateauing of the reaction. Aryl iodides as well as aryl bromides react when equipped with either electron-donating or electron-withdrawing substituents. Aryl chlorides, which contained electron-withdrawing groups, were also reactive under the applied conditions.

/pdf/catalysis-of-a-bis-caffeine-palladium-ii-nhc-pincer-complex-10xqq80n.pdf

Catalysis of a Bis-Caffeine Palladium(II) NHC-Pincer Complex

Today, the internet makes tremendous amounts of data widely available Often, the same information is behind multiple different available data sets This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions For example, social media platforms can contain an abundance of pictures of the same person or object, yet all of which are taken from different perspectives In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise This latter application allows for a rigorous mathematical treatment, which is the content of this contribution We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process In a simplified scenario, we assume that the distorted image is corrupted by noise that acts independently on each pixel We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA) In the case of binary data and binary symmetric noise, we develop a simplified variant of the algorithm, dubbed BUDDA, which we prove to attain universal denoising uniformly

Information Theoretic Principles of Universal Discrete Denoising

In recent years, there have been several fruitful interchanges of methods between the fields of sparse and low-rank recovery on the one hand and quantum information theory on the other hand. One way to understand this seemingly surprising coincidence is that the analysis of vectorand matrix-valued randomized constructions plays an important role in both fields. An example is the realization that certain matrix-valued large deviation bounds can be employed to substantially simplify and generalize the analysis of low-rank matrix recovery schemes. In this workshop, the participants worked to identify and collaborate on further mathematical problems that are being researched in parallel by the two communities. Topics that have been discussed include • Tools for the analysis of vectorand matrix-valued randomized constructions and their application to phase retrieval problems • Conversely, tools for de-randomizing such protocols, based, e.g., on spherical designs. • Uncertainty relations, e.g., for the task of lower-bounding the number of measurements required for signal identification. • Time-frequency methods (known as phase-space methods in physics). • Matrixand tensor norms: computational tools, complexity, relaxations and their application to tensor recovery. Mathematics Subject Classification (2010): 15xx, 15A83, 15A42, 47A52, 46N50. 1048 Oberwolfach Report 18/2014 Introduction by the Organisers The mini-workshop Mathematical Physics meets Sparse Recovery, organised by David Gross (Freiburg), Felix Krahmer (Göttingen), Rachel Ward (Austin), and Andreas Winter (Bellaterra) successfully initiated intensive communication between researchers in two different areas. Among the participants there were, on the one hand, nine researchers focusing on mathematical signal processing, in particular on sparse recovery and related questions, and, on the other hand, seven mathematical physicists who have contributed to quantum information theory. The connection between these fields first started to arise with the works of David Gross, one of the workshop organizers, who demonstrated that certain problems in quantum information theory are closely related to problems in low-rank matrix recovery [1]. So tools developed in mathematical physics can help solve mathematical signal processing problems. Following up on his results, a collaboration between David Gross, his PhD student Richard Küng, also a workshop participant, and Felix Krahmer, another organizer, started [4], strengthening the connection between the fields. This collaboration laid the foundation for the mini-workshop. From their collaboration experience, they realized that one of the biggest obstacles to an intensified collaboration between the fields was the often quite different mathematical language and notation used in the two fields, it was decided that a substantial part of the workshop should be devoted to communicating to the respective other group the way of thinking and the terminology employed. Another substantial part was to be devoted to communicating the general research goals to find collaboration projects, and the third intended pillar was organized discussions in small groups. The workshop started by two introductory talks of about 90 minutes each by participants representing the sparse recovery community. Dustin Mixon gave a general overview of mathematical signal processing problems on a very broad level and Holger Rauhut continued by providing a more technical introduction to the methods currently used. The goal of these two talks was to communicate the type of problems arising in the signal processing community to those participants from quantum information theory who were experts on relevant methods while not having applied them to mathematical signal processing before. Reciprocating, Andreas Winter gave a similar 90 minute talk introducing the problems and mathematical methods at the center of quantum information theory. After these introductions, the workshop proceeded as follows: days were kicked off by a one hour talk requested the previous day. After that, the participants were divided into collections of small, mixed groups that started working on specific questions. Topics that received significant attention by those groups are as follows: Tight large-deviation bounds for sums of random matrices. This theory was essential to set up the connection between the two communities. Originally developed by A. Winter to treat quantum information problems, large-deviation bounds for sums of random matrices were introduced into the theory of sparse and lowrank recovery by D. Gross and later greatly refined at the hands of J. Tropp. Joel Tropp presented the state of the art and the most pressing problems as he Mini-Workshop: Mathematical Physics meets Sparse Recovery 1049 sees the theory. A concrete problem – removing a sometimes spurious logarithmic dimension factor in front of the generally exponentially small large deviation probability – created particular interest. While the problem was not solved during the workshop, collaborations have been initiated as a result. A conjectured “matrix arithmetic-geometric mean inequality.” Recently, a noncommutative extension of the well-known arithmetic-geometric mean inequality for vectors was proposed by B. Recht and C. Ré [2], and this conjecture was communicated to the workshop participants by Felix Krahmer and Rachel Ward. Such an inequality is of interest in machine learning and signal processing as it would give theoretical justification to the observed effect that without-replacement sampling schemes outperform with-replacement sampling schemes in randomized sequential optimization algorithms. Although this inequality has been verified in certain special cases, neither a general proof nor a counter-example has been found. While the conjecture was not resolved during the workshop, Marius Junge made initial discoveries towards finding a counter-example to the conjecture using free probability and recent techniques he had devised for related matrix problems. The nascent theory of tensor recovery. After having treated sparse vectors and low-rank matrices, the signal analysis community has recently turned their attention to the theory of learning low-rank tensors from underdetermined measurements. Tensor problems likewise appear in quantum mechanics, where manybody wave functions are just elements in large tensor spaces. After extremely well-received talks by Y.-K. Liu about applications in natural language processing and by Z. Stojanac on recent ideas for tensor norm relaxations based on theta bodies, several discussions ensued. A mixed group tried to devise measurements that are incoherent w.r.t. all low-rank tensors – generalizing previous such constructions that the quantum community routinely uses for matrices. The prospect of proving results for completely symmetric tensors was discussed. V. Cevher introduced the physicists to dual smoothing techniques that might speed up numerical methods for computing tensor norms. There was an extensive discussion as to whether tests for quantum separability based on symmetric extensions could give rise to well-performing convex proxies for tensor rank. Phase space and time-frequency methods. Inspired by an earlier talk by G. Pfander on time-frquency analysis and sparse recovery, D. Gross presented unpublished work on phase space support-rank uncertainty relations and their role in proving lower bounds to low-rank matrix recovery problems. A collaboration between Gross and Pfander was initiated with the goal to generalize these results from discrete to continuous Gabor systems. Stability of PhaseLift. The ill-defined inverse problem of retrieving an unknown complex vector from “amplitude” measurements – i.e. linear measurements that are ignorant towards complex phases – has received considerable attention in the field of mathematical signal processing over the last few years. Moreover, problems of this type are also of considerable interest for doing quantum state tomography – an important subfield of quantum information theory [5]. During the course of the workshop, H. Rauhut and R. Küng started to tackle the important problem 1050 Oberwolfach Report 18/2014 of proving stability guarantees for PhaseLift in the presence of noise for certain measurement setups – most notably random coded diffraction patterns [6]. Although the problem could not be fully solved during the workshop, partial results have been obtained and yet another ongoing collaboration (between H. Rauhut, R. Küng and D. Gross) arose. In this context, also a connection in the other direction arose, namely F. Krahmer and Y.-K. Liu started a collaboration with the goal to apply mathematical tools developed and applied in the context of phase retrieval problems to problems in quantum information. Statistical trade-offs in low-rank recovery. It had been observed numerically [5] that the performance of low-rank based estimators for quantum state tomography displays the following behavior: Assume the total number of experimental samples taken is constant. There is the freedom to use these samples to either estimate a few linear functions of the unknown low-rank matrix to a high precision, or many distinct functions more coarsely. Maybe surprisingly, it turns out that the performance of the estimator is largely independent of that choice. This is of relevance to physical experiments – but the physicists failed to find a theoretical explanation for this behavior. M. Gutta suggested an approach based on asymptotic properties of the maximum likelihood estimator, while R. Saab proposed to use results about the behavior of right-inverses of near-isometric embeddings to attack the problem. Both ideas seem promising, and a collaboration between the aforementioned researchers, D. Gross and A. Winter to further pursue these questions has been initiated. To conclude, this mini-workshop was by all accounts a great suc

Andreas Winter

Papers

Asymptotic Separation Between Adaptive and Non-adaptive Strategies in Quantum Channel Discrimination

Infinite-Dimensional Programmable Quantum Processors

Catalysis of a Bis-Caffeine Palladium(II) NHC-Pincer Complex

Information Theoretic Principles of Universal Discrete Denoising

Mini-Workshop: Mathematical Physics meets Sparse Recovery