The purpose of these workshops is to bring together an international selection of scientists to discuss the latest developments in Squeezed States in various branches of physics, and in the understanding of the foundations of quantum mechanics. At the third workshop, special attention was given to the influence that quantum optics is having on our understanding of quantum measurement theory. The fourth meeting in this series will be held in the People's Republic of China.
The purpose of these workshops is to bring together an international selection of scientists to discuss the latest developments in Squeezed States in various branches of physics, and in the understanding of the foundations of quantum mechanics. At the third workshop, special attention was given to the influence that quantum optics is having on our understanding of quantum measurement theory. The fourth meeting in this series will be held in the People's Republic of China.
The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory.
This special issue of Journal of Optics B: Quantum and Semiclassical Optics is composed mainly of extended versions of talks and papers presented at the Eighth International Conference on Squeezed States and Uncertainty Relations held in Puebla, Mexico on 9–13 June 2003. The Conference was hosted by Instituto de Astrofísica, Óptica y Electrónica, and the Universidad Nacional Autónoma de México. This series of meetings began at the University of Maryland, College Park, USA, in March 1991. The second and third workshops were organized by the Lebedev Physical Institute in Moscow, Russia, in 1992 and by the University of Maryland Baltimore County, USA, in 1993, respectively. Afterwards, it was decided that the workshop series should be held every two years. Thus the fourth meeting took place at the University of Shanxi in China and was supported by the International Union of Pure and Applied Physics (IUPAP). The next three meetings in 1997, 1999 and 2001 were held in Lake Balatonfüred, Hungary, in Naples, Italy, and in Boston, USA, respectively. All of them were sponsored by IUPAP. The ninth workshop will take place in Besançon, France, in 2005. The conference has now become one of the major international meetings on quantum optics and the foundations of quantum mechanics, where most of the active research groups throughout the world present their new results. Accordingly this conference has been able to align itself to the current trend in quantum optics and quantum mechanics. The Puebla meeting covered most extensively the following areas: quantum measurements, quantum computing and information theory, trapped atoms and degenerate gases, and the generation and characterization of quantum states of light. The meeting also covered squeeze-like transformations in areas other than quantum optics, such as atomic physics, nuclear physics, statistical physics and relativity, as well as optical devices. There were many new participants at this meeting, particularly from Latin American countries including, of course, Mexico. There were many talks on the subjects traditionally covered in this conference series, including quantum fluctuations, different forms of squeezing, unlike kinds of nonclassical states of light, and distinct representations of the quantum superposition principle, such as even and odd coherent states. The entanglement phenomenon, frequently in the form of the EPR paradox, is responsible for the main advantages of quantum engineering compared with classical methods. Even though entanglement has been known since the early days of quantum mechanics, its properties, such as the most appropriate entanglement measures, are still under current investigation. The phenomena of dissipations and decoherence of the initial pure states are very important because the fast decoherence can destroy all the advantages of quantum processes in teleportation, quantum computing and image processing. Due to this, methods of controlling the decoherence, such as by the use of different kinds of nonlinearities and deformations, are also under study. From the very beginning of quantum mechanics, the uncertainty relations were basic inequalities distinguishing the classical and quantum worlds. Among the theoretical methods for quantum optics and quantum mechanics, this conference covered phase space and group representations, such as the Wigner and probability distribution functions, which provide an alternative approach to the Schr\"odinger or Heisenberg picture. Different forms of probability representations of quantum states are important tools to be applied in studying various quantum phenomena, such as quantum interference, decoherence and quantum tomography. They have been established also as a very useful tool in all branches of classical optics. From the mathematical point of view, it is well known that the coherent and squeezed states are representations of the Lorentz group. It was noted throughout the conference that another form of the Lorentz group, namely, the 2 x 2 representation of the SL(2, c ) group, is becoming more prominent while providing the mathematical basis for the Poincaré sphere, entanglement, qubits and decoherence, as well as classical ray optics traditionally based on 2 x 2 `ABCD' matrices. The contributions of this special issue cover the most recent trends in all areas of quantum optics and the foundations of quantum mechanics.
The fourth International Conference on Squeezed States and Uncertainty Relations was held at Shanxi University, Taiyuan, Shanxi, China, on June 5 - 9, 1995. This conference was jointly organized by Shanxi University, the University of Maryland (U.S.A.), and the Lebedev Physical Institute (Russia). The first meeting of this series was called the Workshop on Squeezed States and Uncertainty Relations, and was held in 1991 at College Park, Maryland. The second and third meetings in this series were hosted in 1992 by the Lebedev Institute in Moscow, and in 1993 by the University of Maryland Baltimore County, respectively. The scientific purpose of this series was initially to discuss squeezed states of light, but in recent years, the scope is becoming broad enough to include studies of uncertainty relations and squeeze transformations in all branches of physics, including, of course, quantum optics and foundations of quantum mechanics. Quantum optics will continue playing the pivotal role in the future, but the future meetings will include all branches of physics where squeeze transformations are basic transformation. This transition took place at the fourth meeting of this series held at Shanxi University in 1995. The fifth meeting in this series will be held in Budapest (Hungary) in 1997, and the principal organizer will be Jozsef Janszky of the Laboratory of Crystal Physics, P.O. Box 132, H-1052. Budapest, Hungary.
This special issue is composed mainly of extended versions of talks and papers presented at the Seventh International Conference on Squeezed States and Uncertainty Relations held in Boston, Massachusetts, USA, on 4-8 June 2001. The conference was hosted by Boston University. The first meeting of this kind took place in College Park, Maryland, USA in 1991 as a small workshop. The second and third meetings were held in Moscow, Russia and Baltimore, USA in 1992 and 1993, respectively. The fourth meeting took place in Taiyuan, Shanxi Province, China in 1995 as an international conference sponsored by the International Union of Pure and Applied Physics. The fifth and sixth meetings were held in Balatonfüred, Hungary and Naples, Italy in 1997 and 1999, respectively. The eighth conference will take place in Puebla, Mexico in 2003. The contributions to this special issue address, in the first instance, the foundations of quantum mechanics and quantum optics, and several modern topics which have been intensively developed during the last decade. Quantum fluctuations, squeezing phenomena and different kinds of nonclassical states of light represent some of the most intensively discussed subjects. In particular, several papers deal with the properties of different kinds of `Schrödinger cat states' modelled in the simplest case by the even and odd coherent states. This paradigm exhibits in the most distinct form such cornerstone properties of quantum mechanics as the superposition principle, which manifests itself in quantum interference and entanglement. The quantum entanglement phenomenon has been studied intensively for the past few years due to its importance, for example, in quantum computer projects. In spite of the fact that this concept was known from the beginning of quantum mechanics, its properties, for example, the most appropriate entanglement measures, are still areas of discussion. Another related aspect of quantum nature is teleportation, which is also a subject of intensive study. The phenomena of dissipations and decoherence of the initial pure states are also very important, because fast decoherence can destroy all the advantages of quantum processes in quantum computing, teleportation and image processing. Due to these aspects, papers concerning various methods of controlling the decoherence, for example, by means of using different kinds of nonlinearities and deformations, are also presented here. From the very beginning of quantum mechanics, the uncertainty relations were basic inequalities distinguishing the classical and quantum worlds. Developing a deeper understanding of the well-known uncertainty relations and striving to find new ones (connected with purity parameters of states, entropy, etc.) is an important aspect of modern research. Recently developed tomographic methods of measuring quantum states (in terms of the Wigner function or other phase-space characteristics) have resulted in the formulation of quantum mechanics in which the standard probability density describes the quantum states in an alternative way to the density matrix or wave function. Some papers devoted to tomographic methods of measuring quantum states and studying different sorts of uncertainty relations are presented here. Group-theoretical methods of studying quantum-mechanical and quantum-optical phenomena, including the group-representation description of light polarization, also attract ongoing interest in the conference series discussions. We hope that this special issue will help readers to obtain an overview of the current trends in modern quantum optics, both experimental and theoretical. Young S Kim University of Maryland, College Park, USA Margarita A Man'ko P.N. Lebedev Physical Institute, Moscow, Russia Alexander Sergienko Boston University, MA, USA Guest Editors
Since its conception 90 years ago, the quantum uncertainty principle introduced by Werner Heisenberg lies behind most important features of quantum physics, and its implications have an impact that goes far beyond the physics community. This book focuses on the quantum uncertainty principle, providing an up-to-date examination of recent developments of its applications in quantum information theory. The book brings together several renowned experts working in the foundations of quantum mechanics and quantum information theory. The authors provide different approaches to the study of uncertainty relations and other fundamental aspects of the quantum formalism. Topics addressed include entanglement and Bell inequalities, the application of entropic information measures to the study of uncertainty inequalities, the characterization of deep learning networks in the context of adiabatic quantum computation, and the study of general properties of the set of quantum states. The content of this book will surely benefit both experienced and new researchers specializing in quantum information theory and the foundations of quantum mechanics.