The meeting was attended by over 50 participants from more than 10 countries and three continents. It brought together mathematicians, physicists and computer scientists working on quantum information and computation. Experts were present as well as young participants, both at predoctoral level as well as postdoctoral level. The focus was on the problems of entanglement and decoherence, aiming at the formulation and discussion of precise concepts, developments of models and their interrelations, and the discussion of experiments in relation with the theory. Special attention was given to recent developments, and to furthering interaction and co-operations between the different groups. The scientific programm focused mainly on the following subjects: 1) Quantum Entanglement and Nonlocality: including Bell-type inequalities (theoretical and experimental studies), equivalence of quantum states under local unitary transformations. 2) Quantum Separability: separability criteria for multiple quantum mixed states in arbitrary dimension. 3) Decoherence: study of models; quantum error corrections, fault tolerant computation, multiparticle problems. 4) Sources of Quantum Entanglement. 5) Quantum Information: quantum cloning, teleportation, key distribution, algorithms. 6) Quantum Measurement and Quantum Optics; Holonomic quantum gates; Quantum semigroups; Continuum Observation. 7) Mathematical Quantum and non commutative structures in connection with quantum information theory. 20 lectures were presented, including 15 surveys and 5 concentrating on specific recent results. There were 10 informal evening lectures on 3 topics: entanglement, control and decoherence. Besides 7 informal talks were presented in 2 round table discussions. All presentations and discussions amply demonstrated the vitality and actuality of this area of research and the fascinating interrelations between the different specialities it involves. The organizers and participants would like to take this opportunity to thank the Mathematisches Forschungsinstitut Oberwolfach for having provided a comfortable and inspiring environment for the meeting and the scientific work.
The meeting was attended by over 50 participants from more than 10 countries and three continents. It brought together mathematicians, physicists and computer scientists working on quantum information and computation. Experts were present as well as young participants, both at predoctoral level as well as postdoctoral level. The focus was on the problems of entanglement and decoherence, aiming at the formulation and discussion of precise concepts, developments of models and their interrelations, and the discussion of experiments in relation with the theory. Special attention was given to recent developments, and to furthering interaction and co-operations between the different groups. The scientific programm focused mainly on the following subjects: 1) Quantum Entanglement and Nonlocality: including Bell-type inequalities (theoretical and experimental studies), equivalence of quantum states under local unitary transformations. 2) Quantum Separability: separability criteria for multiple quantum mixed states in arbitrary dimension. 3) Decoherence: study of models; quantum error corrections, fault tolerant computation, multiparticle problems. 4) Sources of Quantum Entanglement. 5) Quantum Information: quantum cloning, teleportation, key distribution, algorithms. 6) Quantum Measurement and Quantum Optics; Holonomic quantum gates; Quantum semigroups; Continuum Observation. 7) Mathematical Quantum and non commutative structures in connection with quantum information theory. 20 lectures were presented, including 15 surveys and 5 concentrating on specific recent results. There were 10 informal evening lectures on 3 topics: entanglement, control and decoherence. Besides 7 informal talks were presented in 2 round table discussions. All presentations and discussions amply demonstrated the vitality and actuality of this area of research and the fascinating interrelations between the different specialities it involves. The organizers and participants would like to take this opportunity to thank the Mathematisches Forschungsinstitut Oberwolfach for having provided a comfortable and inspiring environment for the meeting and the scientific work.
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12–23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy–Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable systems, the second by T Prosen, discussing chaos and complexity in quantum systems. Both topics have theoretical as well as experimental relevance and are likely to witness a fast growing development in the near future. The remaining contributions present more specific and very recent results. They involve the study of the structure of quantum states and their estimation (B Baumgartner et al , C King et al , S Olivares et al , D Petz et al and W van Dam et al ), of entanglement generation and its quantification (G Brida et al , F Ciccarello et al , G Costantini et al , O Romero-Isart et al , D Rossini et al , A Serafini et al and D Vitali et al ), of randomness related effects on entanglement behaviour (I Akhalwaya et al , O Dahlsten et al and L Viola et al ), and of abstract and applied aspects of quantum computation and communication (K Audenart, G M D'Ariano et al , N Datta et al , L C Kwek et al and M Nathanson et al ). We would like to express our gratitude to the European Commission, the Abdus Salam ICTP, SISSA and Eurotech SpA (Amaro, Udine, Italy) for financial and/or logistic support. Special thanks also go to the workshop secretary Marina De Comelli, and the secretaries of the Department of Theoretical Physics, University of Trieste, Sabrina Gaspardis and Rosita Glavina for their precious help and assistance.
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In viewof all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12–23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy–Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two reviewarticles, the first byGAdesso and F Illuminati discussing entanglement in continuous variable systems, the second by T Prosen, discussing chaos and complexity in quantum systems. Both topics have theoretical as well as experimental relevance and are likely to witness a fast growing development in the near future. The remaining contributions present more specific and very recent results. They involve the study of the structure of quantum states and their estimation (B Baumgartner et al, C King et al, S Olivares et al, D Petz et al and W van Dam et al), of entanglement generation and its quantification (G Brida et al, F Ciccarello et al, G Costantini et al, O Romero-Isart et al, D Rossini et al, A Serafini et al and D Vitali et al), of randomness related effects on entanglement behaviour (I Akhalwaya et al, O Dahlsten et al and L Viola et al), and of abstract and applied aspects of quantum computation and communication (K Audenart, G M D'Ariano et al, N Datta et al, L C Kwek et al and M Nathanson et al). We would like to express our gratitude to the European Commission, the Abdus Salam ICTP, SISSA and Eurotech SpA (Amaro, Udine, Italy) for financial and/or logistic support. Special thanks also go to the workshop secretary Marina De Comelli, and the secretaries of the Department of Theoretical Physics, University of Trieste, Sabrina Gaspardis and Rosita Glavina for their precious help and assistance.
Quantum entangled states play very important roles in quantum information processing,such as quantum teleportation,dense coding,error correction,cryptography,and computation.The theory of entanglement mainly concerns the characterization of quantum entanglement and the classification of quantum states,as well as its applications in quantum information processing.We present some basic concepts and results,including:the relationship between locality and reality in quantum mechanics and Bell inequalities,and that between Bell inequalities and the separability of quantum states;the definition of separability for pure and mixed quantum states,and some separability criteria such as the positive map approach,positive partial transpose,reduction criterion,realignment,entanglement witnesses,and the covariance matrix approach and local uncertainty relations;some entanglement measures such as the entanglement of formation,concurrence,relative entropy,negativity,tangle,entanglement of assistance,and their estimation;the change in entanglement when the physical system evolves or undergoes interaction with the environment.
Guest Editors During the past two decades, there has emerged the new subject of quantum information and computation which both offers the possibility of powerful new modes of computing and communication and also suggests deep links between the well established disciplines of quantum theory and information theory and computer science. In recent years, the growth of the subject has been explosive, with significant progress in theory and experiment. The area has a highly interdisciplinary character with contributions from physicists, mathematicians and computer scientists in particular. Developments have occurred in diverse areas including quantum algorithms, quantum communication, quantum cryptography, entanglement and nonlocality. This progress has been reflected in contributions to Journal of Physics A: Mathematical and General which traditionally provides a natural home for this area of research. Furthermore, the journal's committment to this field has recently been strengthened by the appointments of Sandu Popescu and Nicolas Gisin to the Editorial Board, and in this special issue we take the opportunity to present a snapshot of the present state of the art.
The conference brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantically methods, and other computer science techniques applied to the study of physical behaviour in general. Work that applies structures and methods inspired by quantum theory to other fields (including computer science) is also welcome. With members from around the world focused on Quantum physics and Nuclear Engineering this is your best opportunity to reach the largest assemblage of participants from the universities, colleges, research centres, societies, institutions, labs, associations, communities and companies etc. We want to make a worldwide meet in which data between researchers from the different controls can be effectively traded. The explanation behind bringing the general population at the meetings together is to catalyse empowering trades and connections between experts in different fields, from physical science to engineering. It will make new interdisciplinary systems and permit members to trade know-how and data to accomplish speedier and better results.
Information is a physical. Physical systems register and process information. These facts generated enormus interest in the development of novel quantum tecnologies, especially because the construction of smaller electronic devices ultimately leads to a consideration of quantum mechanical effects in electronic and computer desingns. The notion of the classical bit of information theory was formally pushed into the realm of the quanta with the introduction of the quantum bit or qubit, in the seminal works of Deutsch (Deutsch, 1985) and Shor (Shor, 1994). They demostrated that, indeed, controlled multipartite qubit interference effects could provide the means for a radical new way of computing, allowing the computation of many intractable computational problems, such as the factoring of large number or exact simulation of large quantum systems. The field of experimental and theoretical research in quantum information and computation has emerged as very important player in the understanding of quantum phenomena the both the basic and technological levels. This has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineerin, to the physical sciences, and we now have an interdisciplinary field where great efforts are being made in order to build devices that allow the progressing of information at a quantum level. A concise introduction to the field of quantum information and quantum computation is presented. This stars with the bassic definitions of bits, quantum registers, through to the universal gate-set for building the universal quantum computer, from a quantum network model of computation. The work shows how two-qubit gates suffice for quantum computation, emphasing the power of the quantum circuit representation for entagling and disentagling quantum states. This leads to the “no-cloning theorem”, which leads us to many interesting applications, such as quantum cryptography. Two alternative approaches or performing quantum computation are also described i) the one-way or measurement based quantum computer method, and ii) holonomic or geometric quantum computation. Following this, quantum entaglement quantification is highlighted, particulary its usefulness as a communication resource, in order to describe some of its most celebrated practical applications to date: quantum teleportation, cryptography, dens coding, and data compression. Deutsch’s concept of quantum parallelism is enphasized in order to gain insight into the potential for efficiently solving certain classically intratable algorithms. A subject central to the field of QIP- quantum decoherence- is then introduced.. Possible ways to overcome it, in particular quantum error correction, are discussed. A descriptios of some of the currently available hardware of the practical implementation of quantum computation is provided with a discussion of the main physical quantum bits that are currently employed (or proposed) for a such a purpose.