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The principle of complementarity is one of the cornerstones of quantum theory. The aim of this study was to advance our understanding of complementarity by analyzing the role of delayed choice and quantum erasers in two-slit experiments, and by proposing experiments for verifying the analysis. The analysis is based on models consisting of measurable spaces and probability measures involved in the experiments. The main findings are as follows: (a) The complementarity principle manifests itself in such a way that wave and particle behaviors cannot be simultaneously observed almost surely with respect to any single, fixed measure. (b) Described by different measures, complementary properties can coexist in the same experimental setup. (c) Which-way information will not preclude or erase interference fringes. (d) Delayed choice and quantum erasers are irrelevant to testing complementarity. (e) It is possible for us to know through which slit each quantum object passed almost surely with respect to the measure corresponding to the slit while the interference pattern is intact. Based on the experiments analyzed, realizable experiments are proposed for verifying the above results.

Complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For a completely incoherent state, it is known that wave and particle quantifiers can reach zero, and hence no information about the wave and particle aspects of the system can be obtained. This means that the information is being shared with another systems, and quantum correlations can be seen as responsible for the loss of purity of the quanton, provided that the quanton is part of a multipartite pure quantum system. In this paper, by exploring the purity of bi- and tri-partite pure quantum states, we show that it is possible to obtain complete complementarity relations. This procedure allows us to create a general framework for obtaining complete complementarity relations for a subsystem that belongs to an arbitrary multi-partite quantum system in a pure state. Besides, by some simple examples, we show that if the predictability measure is changed then the correlation measure must also be changed in order to obtain complete complementarity relations for pure cases., Comment: 13 pages, 6 figures. Accepted for publication in Journal of Physics A: Mathematical and Theoretical

The problem of approximate joint measurement of complementary observables, like position and momentum, and the relevance of the uncertainty relations to that question were at the heart of the investigations of Paul Busch into the foundations of quantum mechanics. A good third of his published work dealt with this and closely related questions. This paper is an attempt to survey some of the steps taken in that research starting with Paul’s first papers on the subject matter in the early 1980’s and reaching its height in recent years.

The weighted complementarity problem is an extension of the standard finite dimensional complementarity problem. It is well known that the smoothing-type algorithm is a powerful tool of solving the standard complementarity problem. In this paper, we propose a smoothing-type algorithm for solving the weighted complementarity problem with a monotone function, which needs only to solve one linear system of equations and performs one line search at each iteration. We show that the proposed method is globally convergent under the assumption that the problem is solvable. The preliminary numerical results indicate that the proposed method is effective and robust for solving the monotone weighted complementarity problem.

The rapid development and large-scale utilization of clean energy is not only conducive to alleviate the global fossil energy crisis, but also brings huge economic and environmental benefits. However, the uncertainty of new energy represented by wind power and photovoltaic power brings a lot of impact on the operation and dispatching of the power system. Hence, it’s urgent to explore a new dispatching mode adapted to the power system with high proportion of clean energy. The optimal dispatching method of power system with high proportion clean energy based on multi-energy complementarity is explored with goal of making full use of clean energy and reducing the operating cost. Particle swarm optimization algorithm and branch and bound method are used to solve the cascade hydropower optimal dispatching problem and the wind, photovoltaic, thermal power joint optimal dispatching problem respectively. Finally, the feasibility of the model is verified by an example.

This paper presents a conceptual study of ASEAN countries, explore the possibility of developing carbon trading futures and options market from an economic perspective. Owing to market-based complementarity and an invisible hand in the economic market to influence the market and the difference in the development level of ASEAN countries, the joint planning of carbon trading mechanism (carbon trading emission rights mechanism) has become a great trend in the future. The ASEAN countries are currently at a stage of high industrial development; it also brings many pollution problems. How to maintain economic stability and even growth without prejudice to the environment is one aspect of the hard work of scholars studying environmental protection and economists jointly. This paper sets a framework for a carbon trading mechanism to study what impact it will have on the market economy and the environment. It is hoped that this creative idea will be realized and benefited mankind and nature in the future.

We first present, by using exclusivity principle, a brief proof of the complementarity principle: the sum of squared expectation values of dichotomic (±1) mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny's inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations.

Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there is a direct link between them. In this work, we propose a definition of intrinsic concurrence for two-qubit states. Although the intrinsic concurrence is not a measure of entanglement, it embodies the concurrence of four pure states which are members of a special pure state ensemble for an arbitrary two-qubit state. And we show that intrinsic concurrence is always complementary to first-order coherence. In fact, this relation is an extension of the complementary relation satisfied by two-qubit pure states. Interestingly, we apply the complementary relation in some composite systems composed by a single-qubit state coupling with four typical noise channels respectively, and discover their mutual transformation relation between concurrence and first-order coherence. This universal complementarity provides reliable theoretical basis for the interconversion of the two important quantum resources.

Electrical tomography (ET) and ultrasonic tomography (UT) techniques are effective and promising super-sensing tools with uses in many industrial process applications. They can create internal mapping images of both electrical and mechanical properties from measurements at the exterior boundaries of domains of interests. There are several different types of ET methods and different modes of UT imaging. Here we focus on contactless ET and contactless UT imaging for liquid masses, enabling fully non-intrusive, integrated mechanical and electrical imaging because direct contact to the process material is often a major limiting factor. ET is sensitive to the distribution of dielectric parameters inside the region of interest, and the highest sensitivity often lies near the outer surface of the boundary. UT has very good responses to the intersections of different phases of materials and has the highest resolution in the central area. Capacitively coupled electrical impedance tomography (CCEIT) is proposed as a contactless ET technique. This work investigates CCEIT based on phase measurements of the electrical impedance between transmitting and receiving electrodes, and UT based on the transmission mode, measuring the time-of-flight between the transmitted signal and the first received signals. A combined sensor which comprises a 16-electrode CCEIT array and a 16-transducer UT array is developed. Experimental results show the performances of the two tomography systems and their dual modality combination. This work highlights various aspects of the correlation, comparison and complementarity between these two contactless imaging techniques. Inclusion material characterization and identification is demonstrated using this novel dual modality.

Classical mechanics is based on the notion that matter consists of persistent particles that can be reidentified (or tracked) across time. However, the mathematical symmetrization procedures (due to Dirac (1926 Proc. R. Soc. A 112 661) and Heisenberg (1926 Z. Phys. 38 411) and Feynman (1965 Quantum Mechanics and Path Integrals 1st edn (New York: McGraw-Hill))) used to describe identical particles within the quantum formalism are widely interpreted as implying that identical quantum particles are not persistent (so that the concept of ‘the same particle’ is not meaningful) or are persistent but not reidentifiable. However, it has not proved possible to rigorously reconcile these interpretations with the fact that identical particles are routinely assumed to be reidentifiable in particular circumstances—for example, a track in a bubble chamber is interpreted as a sequence of bubbles generated by one and the same particle (Mirman 1973 Il Nuovo Cimento 18B 110; de Muynck 1975 Int. J. Theor. Phys. 14 327; Dieks and Lubberdink 2011 Found. Phys. 41 1051; Jantzen 2011 Phil. Sci. 78 39). Moreover, these interpretations do not account for the mathematical form of the symmetrization procedures, leaving open theoretical possibilities other than bosonic and fermionic behavior, such as paraparticles (Messiah and Greenberg 1964 Phys. Rev. 136), which however do not appear to be realized in nature. Here we propose that the quantum mechanical behavior of identical particles is a manifestation of a novel kind of complementarity, a complementarity of persistence and nonpersistence. Accordingly, identical ‘particles’ are neither persistent nor nonpersistent; rather, these terms are to be understood as descriptors of different models of the same experimental data. We prove the viability of this viewpoint by showing how Feynman’s and Dirac’s symmetrization procedures arise through a synthesis of a quantum treatment of persistence and nonpersistence models of identical particle-like events, and by showing how reidentifiability emerges in a context-dependent manner. Finally, by drawing on a reconstruction of Feynman’s formulation of quantum theory (Goyal et al 2010 Phys. Rev. A 81 022109), we construct a precise parallel between the proposed persistence–nonpersistence complementary and Bohr’s wave–particle complementarity for individual particles, and detail their conceptual similarities and dissimilarities.

We study the fringe visibility and the which-path information (WPI) of a general Mach–Zehnder interferometer with an asymmetric beam splitter (BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI Ipath are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship V 2 + I path 2 ≤ 1 is found, and the conditions for equality are also presented.

Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is no state-independent "reality trade-off" between noncommuting observables, as in certain systems all observables are real [Europhys. Lett. 112, 40005 (2015)]. We show that the entropic uncertainty relation in the presence of quantum memory [Nature Phys. 6, 659 (2010)] perfectly supplements the discussed notion of reality, rendering trade-offs between reality and quantum uncertainty. State-independent complementarity inequalities involving entropic measures of both, uncertainty and reality, for two observables are presented., Comment: Published in Special Volume "Shannon's Information Theory 70 years on: applications in classical and quantum physics"

A detailed account is presented of the Doppler effect as a photon phenomenon, complementing a recent paper by Giuliani (2013 Eur. J. Phys. 34 1035–47). The essence of Schrodinger's pioneering derivation (1922 Phys. Z. 23 301–3) of a Doppler formula in terms of the corpuscular theory of light, using energy–momentum conservation, is related. Some neglected references that put the whole scene around the Ives–Stilwell experiment into a more precise perspective are highlighted. Atoms as clocks and particle–wave complementarity are also discussed briefly.

Northern Peru is threatened by the consequences of a natural phenomenon called "El Nino", mainly during the months of December to April. In the summer of 2017, this event reported strong climatic variations with intense rains, increasing the water levels of the Chira and Piura rivers, filling the Poechos reservoir, together with flooding and mudding. However, from an energetic perspective, these climatic alterations have a strong potential to increase the availability of the wind and hydro renewable energies in northern Peru. This work performs an evaluation of the hydro-eolic complementarity as part of the sustainability of energy systems. The study includes evaluation of historical records of wind velocity and water flow rates. It then evaluates correlation, analysis, and estimates the hydro and wind energy potentials generated by this phenomenon. The implications of the "El Nino" phenomenon are mostly negative. Nonetheless, it is possible to take advantage of higher wind and water flow rates with a hybrid energy system. The results obtained show a high degree of complementarity both normal and "El Nino" phenomenon condition in northern Peru.

In this paper, we determine the complementarity relations for pure quantum states of N qubits by presenting the definition of local and non-local forms. By comparing the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters, we prove that there exist strict monogamy laws for quantum correlations in all many-qubit systems. Further, the proper form of general entanglement monogamy equality for arbitrary quantum states is found with the characterization of total quantum correlation of qubits. These results may open a new window for multi-qubit entanglement.

We show the information-theoretic security proof of the differential-phase-shift (DPS) quantum key distribution (QKD) protocol based on the complementarity approach [arXiv:0704.3661 (2007)]. Our security proof provides a slightly better key generation rate compared to the one derived in the previous security proof in [arXiv:1208.1995 (2012)] that is based on the Shor-Preskill approach [Phys. Rev. Lett. ${\bf 85}$, 441 (2000)]. This improvement is obtained because the complementarity approach can employ more detailed information on Alice's sending state in estimating the leaked information to an eavesdropper. Moreover, we remove the necessity of the numerical calculation that was needed in the previous analysis to estimate the leaked information. This leads to an advantage that our security proof enables us to evaluate the security of the DPS protocol with any block size. This paper highlights one of the fundamental differences between the Shor-Preskill and the complementarity approaches., 15 pages, 5 figures

This working group focused mainly on the complementarity among particle physics and astrophysics. The analysis of data from both fields will better constrain theoretical models. Much of the discussion focused on detecting dark matter and susy particles, and on the potential of neutrino and gamma-ray astrophysics for seeking or constraining new physics.

I highlight some main aspects of the present complementarity in looking for new physics beyond the Standard Model between accelerator physics and direct and indirect dark matter searches.

A scheme for an atomic beam quantum self-eraser is presented. The proposal is based on time reversal invariance on a quantum optical Ramsey fringes experiment, where a realization of complementarity for atomic coherence can be achieved. It consists of two high finesse resonators that are pumped and probed by the same atom. This property relates quantum erasing with time reversal symmetry, allowing for a full quantum erasing of the which-way information stored in the cavity fields. The outlined scheme also prepares and observes a non-local state in the fields of the resonators: a coherent superposition between correlated states of macroscopically separated quantum systems. The proposed scheme emphasizes the role of entanglement swapping in delayed-choice experiments. Finally, we show that the quantum self-eraser violates temporal Bell inequalities and analyze the relation between this violation and the erasability of which-way information., 13 pages, 4 figures

We critically analyze the problem of formulating duality between fringe visibility and which-way information, in multibeam interference experiments. We show that the traditional notion of visibility is incompatible with any intuitive idea of complementarity, but for the two-beam case. We derive a number of new inequalities, not present in the two-beam case, one of them coinciding with a recently proposed multibeam generalization of the inequality found by Greenberger and YaSin. We show, by an explicit procedure of optimization in a three-beam case, that suggested generalizations of Englert's inequality, do not convey, differently from the two-beam case, the idea of complementarity, according to which an increase of visibility is at the cost of a loss in path information, and viceversa., 26 pages, 1 figure, substantial changes in the text, new material has been added in Section 3. Version to appear in J.Phys. A

We show that number and canonical phase (of a single mode optical field) are complementary observables. We also bound the measurement uncertainty region for their approximate joint measurements.

In the proposed quantum optical experiment, the complementarity and entanglement exhibited in quantum non-demolition (QND) measurement of coherent state superposition is analysed. This problem can be considered as a continuously variable analogue of the well known exhibition of complementarity in Young's double-slit interferometer. Analysis of the relationship between distinguishability and interference in phase space, as well as quantum entanglement, is performed using directly measurable quantities obtained using homodyne detection.

We tested wave-particle duality with the ensemble-averaged spin states of C-13 nuclei in (CHCl3)-C-13 using the spin states of H-1 nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.

We show that for multipath quantum interferometers the visibility of the interference and `which-path' information are not always complementary observables. This implies that there are path measurements that do not destroy the interference.

The discussion of particle-wave dualism still plays an important part in teaching quantum theroy. This surely is for historical reasons, since it was important in grasping the concept of uncertainty. Recent EPR-like experiments, however, indicate new ways of teaching the notions of uncertainty and complementarity. These allow us to achieve a clear understanding without difficult mathematical obstacles and promote also a well-founded discussion of philosophical aspects. The core of the considerations presented here are systems consisting of two-state objects, for example the spin states of photons or electrons.

Wave-like and particle-like features are identified for entangled coherent states, analogous to those identified for single-photon states. A generalized interferometer is introduced for testing complementarity with entangled coherent states.

The possibility of using muon tracking and timing measurements for the reconstruction of the EAS hadron longitudinal development in the knee energy region is discussed. Simulation results are presented which indicate that, provided these measurements are used as complementary and with reasonable TTC (`time-track complementarity') selection, the accuracy of the muon production height reconstruction is sufficiently good even for sub-GeV energy muons, observed at sea level. Possible applications and advantages of the TTC approach in the study of primary cosmic rays and high-energy interactions are discussed.

Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum–classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.

Complementarity and the commutation relation of position (x) and momentum (p) imply much more than the fundamental x-p uncertainty inequality. Here, we display some further consequences of the former that could have certain pedagogical interest and, so, contribute to the teaching of quantum mechanics. Inspired by an elementary derivation of the x-p uncertainty inequality, based upon a positive quadratic polynomial, we explore one possible extension, via quartic polynomials and simple algebra and integrations. Our analysis, aimed at providing some further pedagogic expression of genuine quantum behaviours, yields other quantum inequalities for expectation values, expressed through suitable discriminants associated with quartic algebraic equations, which differ from (and are not a strict consequence of) the x-p uncertainty inequality. Those quantum inequalities are confirmed, and genuine non-classical behaviours are exhibited, for simple cases: a harmonic oscillator, a hydrogenic atom and free Gaussian wave packets. The physical interest of the expectation values involved in the quantum inequalities and of the latter is discussed, in the framework of quantum optics and squeezing phenomena.

The complementarity relationship (also termed duality) that arises between the irreps of the su(3) and u(2) Lie algebras when their direct sum su(3)(+)u(2) is embedded into a larger u(6) algebra and single-row irreps of the latter are considered is extended to the corresponding q-algebras suq(3) and uq(2). It is demonstrated by explicitly constructing the unique q-boson state that is simultaneously maximal in suq(3) and uq(2) for a given u q(2) weight. In addition, the relations between the suq(3) and uq(2) Casimir operators resulting from their complementarity are explicitly found. Together with the q-Bargmann representation of q-boson operators, the complementarity relationship is then used to construct a Gel'fand-Tseitlin basis for arbitrary suq(3) irreps in terms of q-boson operators.

In this paper a chiral composite preon model with semisimple metacolor gauge group E(6)×SU(5) is constructed based on the extended MTCT composite theory. This model predicts 4 generations of quarks and leptons. At low energy region the mass degeneracy between different generation fermions can be broken partly.

January 2014 saw the congregation in Abingdon (UK) of scientists from across the world, to discuss the current state and future of spectroscopy using epithermal neutrons. This meeting was the sixth in a series of workshops held in collaboration between the Science and Technology Facilities Council (UK) and the Consiglio Nazionale delle Ricerche (Italy), aimed at bringing together researchers with an interest in the use of electron-volt neutrons in spectroscopic studies [1]. This technique is termed Deep Inelastic Neutron Scattering (DINS), and also Neutron Compton Scattering (NCS) in reference to the analogy with Compton scattering of X-rays from electrons. In particular, this meeting centred jointly around experimentalists and theoreticians, formulating animated discussions as to the current overview of DINS and future horizons facing the field. The use of electron Volt neutrons for spectroscopic measurements dates back to the advent of proton-driven spallation neutron sources in the 1970s and 1980s. Following an initial scientific meeting in Los Alamos (USA) [2], the first two meetings in this series were held in Abingdon (UK) in 1995 and 1998, with subsequent meetings held in Santa Fe (USA) in 2005 [3], Oak Ridge National Laboratory (USA) in 2006 [4], and Rome, Italy; in 2010 [5]. The flagship instrument serving a continual user-programme for DINS measurements, and the main focus of this meeting, has been the VESUVIO spectrometer at ISIS [6, 7]. Subsequent instruments like SEQUOIA in the USA [8, 9] and a newer spectrometer in the Bariloche LINAC in Argentina [10, 11] have also been commissioned and began serving a growing user community. The availability of DINS measurements has extended the range of possible spectroscopic techniques that utilise neutrons into the kinematic region of high energy and momentum transfers, shown schematically in Figure 1. Spectroscopic instrument suites such as that of ISIS are thus able to probe processes on timescales across nine orders of magnitude, from quantum tunnelling and molecular diffusion up to nuclear recoil under the impulse approximation. DINS is one of the most direct techniques for probing nuclear quantum dynamics in condensed matter, with the ability to measure nuclear kinetic energies and momentum distributions of light nuclei. A major theme for current DINS research relates to the study of nuclear quantum effects, particularly regarding the non-classical behaviour of hydrogen or deuterium. This emphasis was reflected by the meeting's opening session dealing with the measurement of momentum distributions in hydrogen-bonded and aqueous systems (see Table 1). Whilst concentrating on experimental studies, data were presented from the outset alongside state-of-the-art path-integral molecular dynamics (PIMD) calculations, affording an animated discussion as to the interpretation of measured neutron Compton profiles in spatially disordered systems. The extension of DINS to heavier nuclei was visited in the second session of the meeting, under the over-arching theme of MAss-selective Neutron SpEctroscopy (MANSE). The ability of DINS to examine atomically distinct species in condensed matter has garnered interest from the chemistry and materials communities, with both binary systems and more complex materials being presented in this session. Nuclei of interest in applied materials research were highlighted, including oxygen, lithium and fluorine, alongside an assessment of current capabilities and future developments in their examination by DINS. The concluding session of the first day of the meeting was concerned with instrumentation. The detection of epithermal neutrons requires technologies unique relative to their lower-energy counterparts, and the first talk of this session outlined how detector capabilities on existing instruments has been revolutionised in recent years. Resonance detectors and techniques involving analyser-foil cycling were detailed, explaining how they have improved not only the count-rate but also the spectral resolution of instruments such as VESUVIO. Beyond NCS, the detection of nuclear resonances were also considered. An overview of VESUVIO (a time-of-flight instrument operating in so-called indirect geometry) was then given, alongside ways it could be improved upon in light of growing demands from the user community. This discussion was complemented by a presentation of the use of direct-geometry instruments such as SEQUOIA for DINS measurements, highlighting the complementarity with parallel studies on VESUVIO. The second day of the meeting was given over to the theoretical aspects of nuclear momentum distributions. Delegates were presented with the manner in which we can computationally incorporate nuclear quantum effects, along with their output in terms of 'measureables', relating to a varied range of systems. Results were presented from hydrogen-bonded liquids, ferroelectric materials, biological systems, and mixed bosonic-fermionic calculations. The ability to now approach experimental measurement with theoretical insight, and vice versa, is a sea-change in research into nuclear quantum effects. This field is a high-profile area in chemical physics and materials research, and a concerted approach by theory and experimentation allows us to explore and explain the dynamical state of matter at the atomic level in a manner previously unobtainable. Concluding each session throughout the meeting were periods of open discussion, wherein all present could comment or expand upon themes arising from the preceding talks. These discussions were then further distilled and clarified during the final section of the meeting, the 'Frontiers and Horizons' discussion, open to all present to delineate the next steps in DINS as a whole. Experimentalists and theoreticians were able to present their views on how each community could move forward to complement each other, not only separately but with specific projects and milestones in mind. These discussions have been included within these proceedings to highlight the future outlook of DINS. It is the hope of these editors that this meeting will allow spectroscopy with epithermal neutrons to further develop, explaining the very quantum nature of dynamics in condensed matter. Bringing together, as it did, international researchers in fields at the frontiers of their respective experimental and theoretical communities, we hope that the next meeting in this series will see the fruition of concepts and projects instigated by this one.

This article explores Bohr's argument, advanced under the heading of 'complementarity,' concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr's thinking, under the impact of the development of quantum theory and Bohr's confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr's interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr's sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions.

Bohr's intellectual journey began with the recognition that empirical phenomena implied the breakdown of classical mechanics in the atomic domain; this, in turn, led to his adoption of the 'quantum postulate' that justifies the 'stationary states' of his atomic model of 1913. His endeavor to develop a wider conceptual framework harmonizing both classical and quantum descriptions led to his proposal of the new methodological goals and standards of complementarity. Bohr's claim that an empirical discovery can demand methodological revision justifies regarding his epistemological lesson as supporting a naturalistic epistemology.

The least upper bound in Cirel'son's quantum generalization of the local-realistic Bell inequality is intermediate between the local-realistic and general probablistic limits. An alternative derivation of Cirel'son's inequality is presented which sheds light on the role played by complementarity in determining this bound and the fact that it falls short of the general probablistic limit.

We explain briefly why Compton scattering from a crystal gives a featureless continuous x-ray background while Bragg scattering from the same crystal produces sharp diffraction peaks. It is shown that the answer lies at the heart of quantum mechanics, namely the uncertainty and the complementarity principles.

Bohmian mechanics also known as de Broglie-Bohm theory is the most popular alternative approach to quantum mechanics. Whereas the standard interpretation of quantum mechanics is based on the complementarity principle Bohmian mechanics assumes that both particle and wave are concrete physical objects. In 1993 Peter Holland has written an ardent account on the plausibility of the de Broglie-Bohm theory. He proved that it fully reproduces quantum mechanics if the initial particle distribution is consistent with a solution of the Schrodinger equation. Which may be the reasons that Bohmian mechanics has not yet found global acceptance? In this article it will be shown that predicted properties of atoms and molecules are in conflict with experimental findings. Moreover it will be demonstrated that repeatedly published ensembles of trajectories illustrating double slit diffraction processes do not agree with quantum mechanics. The credibility of a theory is undermined when recognizably wrong data presented frequently over years are finally not declared obsolete.

`Mathematical physics' is an extremely broad subject, and the days when one person could be conversant with all its aspects have long since passed. Hence a conference as sweeping as this one is apt have something for everyone, but not enough for anyone. Overviews can be valuable, though, and while this book is not the place to learn anything in depth, it offers a collection of useful signposts pointing towards new ideas to learn and places to learn them. These Proceedings contain papers from 11 sessions and a round table on physics and mathematics, as well as about 20 articles from a satellite conference, `Topology, Strings, and Integrable Models'. Readers of Classical and Quantum Gravity may be especially interested in two sessions. A short section on general relativity includes an article by Bartnik on the construction of exact solutions to the Einstein constraint equations and a very nice (but brief) review by Choptuik of critical behaviour in gravitational collapse. A second section, on strings and quantum gravity, includes a noteworthy (although again brief) paper by Erik Verlinde on black-hole complementarity. I especially enjoyed reading the plenary lectures, which appear at the beginning of the volume. These vary greatly in complexity, from Atiyah's beautiful but elementary introduction to knots and quantum physics to Connes' much denser and more technical discussion of noncommutative geometry. Kontsevich describes rigorous results in the quantum theory of topological sigma-models; Witten reports on recent progress in understanding duality in supersymmetric Yang - Mills theory; Yau offers a survey of mirror symmetry and Damour reviews the experimental status of general relativity. Some of the papers in this section make for good browsing, as well: I know very little about Solar System modelling, for example, but I was fascinated by Laskar's summary of the evidence for chaotic behaviour in planetary orbits. I am not sure a volume like this belongs on a typical physicist's bookshelf, it is a bit too general, and the articles are a bit too terse, to be of day-to-day use, but I would certainly want a copy in my university library.

We study deviations from tri-bimaximality (TBM) and quark-lepton complementarity (QLC) in a model independent way. The current neutrino experimental data is well approximated by tri-bimaximal generation mixing but the QLC relations are not satisfied with each data of 1$\sigma$ level. This means that there exist deviations from the complementarity. The same fact for the TBM might be checked in the future neutrino experiments. We discuss such deviations from the TBM and QLC, simultaneously. A new ratio between the deviations is introduced, and some interesting points are presented. We also show predicted correlations among leptonic mixing angles at the points., Comment: 10 pages, 9 figures, final version

A proposal for resolution of the information paradox is that "nice slice" states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information *problem*, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity., 11 pages of text and figures, + references. v2 minor text. v3 small revisions to match final journal version

The China Advanced Research Reactor (CARR) and the China Spallation Neutron Source (CSNS), like other big national facilities for basic research in China, are viewed as vehicles for engaging in international R&D efforts, furthering the nation's technological advancement, and facing arduous challenges such as energy and materials needs. In 2009, CARR – a 60MW steady-state reactor in Beijing – is expected to reach criticality while the CSNS – an 120 kW pulsed source in Dongguan – is to begin construction. In spite of the differing schedule, the road leading to full operation of the sources and productive utilization of the neutron instruments will be a long one. From the outset both projects benefit a great deal through interactions with the worldwide neutron communities. An even more trenchant task is to build a domestic user base, presumably from China's numerous universities and research laboratories, to imbue new scientific ideas into using and exploiting of the neutron methodology. Arguably, a smaller neutron facility yet apt at flexibility and optimization for education and academic R&D is needed to bridge 'big' facilities and 'small' sciences. Here, we introduce the plan of a compact pulsed neutron source (driven by a 13MeV-proton accelerator system with a Be target and room-temperature and cryogenic moderators), to be built in about 3 years as a part of a Hadron Application Research Center at Tsinghua University. We discuss the mission of these neutron sources, the complementarity therein, and their synergetic relation with the academia and other facilities, and possible cooperation with international counterparts.

Qubits exhibit extreme nonlocality when their state is maximally entangled and this is observed by mutually unbiased local measurements. This criterion does not hold for the Bell inequalities of high-dimensional systems (qudits), recently proposed by Collins–Gisin–Linden–Massar–Popescu and Son–Lee–Kim. Taking an alternative approach, called the quantum-to-classical approach, we derive a series of Bell inequalities for qudits that satisfy the criterion as for the qubits. In the derivation each d-dimensional subsystem is assumed to be measured by one of d possible measurements with d being a prime integer. By applying to two qubits (d=2), we find that a derived inequality is reduced to the Clauser–Horne–Shimony–Holt inequality when the degree of nonlocality is optimized over all the possible states and local observables. Further applying to two and three qutrits (d=3), we find Bell inequalities that are violated for the three-dimensionally entangled states but are not violated by any two-dimensionally entangled states. In other words, the inequalities discriminate three-dimensional (3D) entanglement from two-dimensional (2D) entanglement and in this sense they are genuinely 3D. In addition, for the two qutrits we give a quantitative description of the relations among the three degrees of complementarity, entanglement and nonlocality. It is shown that the degree of complementarity jumps abruptly to very close to its maximum as nonlocality starts appearing. These characteristics imply that complementarity plays a more significant role in the present inequality compared with the previously proposed inequality.