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

This review covers the latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special emphasis on its practical aspects and applications in quantum-information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics is discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode-matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.

https://arxiv.org/pdf/quant-ph/0511044.pdf

Continuous-variable optical quantum-state tomography

Thank you for downloading mathematical methods of statistics. Maybe you have knowledge that, people have search numerous times for their favorite novels like this mathematical methods of statistics, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their laptop. mathematical methods of statistics is available in our book collection an online access to it is set as public so you can download it instantly. Our books collection spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the mathematical methods of statistics is universally compatible with any devices to read.

Mathematical Methods Of Statistics

心臓病診療プラクティス 16. 心不全を癒す

Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research-quantum information versus machine learning (ML) and artificial intelligence (AI)-have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our 'big data' world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement-exploring what ML/AI can do for quantum physics and vice versa-researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.

https://iopscience.iop.org/article/10.1088/1361-6633/aab406/pdf

Machine learning & artificial intelligence in the quantum domain: a review of recent progress.

We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.

https://arxiv.org/pdf/quant-ph/0611244.pdf

Diluted maximum-likelihood algorithm for quantum tomography

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states, provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are also considered.

https://arxiv.org/pdf/quant-ph/0210146.pdf

Quantum inference of states and processes

Preface. 1. Introduction. 2. Fundamentals of quantum theory. 3. Quantum theory of measurement. 4. Coherent states. 5. Nonclassical optical phenomena and their relations. 6. Photon interferences and correlations. 7. Quantum optical and Bell's inequalities. 8. Quantum optical experiments supporting quantum theory. 9. Conclusions. References. Index.

Quantum optics and fundamentals of physics

Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting structure of such estimators will also be explored.

Quantum-state reconstruction by maximizing likelihood and entropy.

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramer-Rao bound.

Zdeněk Hradil

Papers

Diluted maximum-likelihood algorithm for quantum tomography

Quantum inference of states and processes

Quantum optics and fundamentals of physics

Quantum-state reconstruction by maximizing likelihood and entropy.

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.