Search

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure v from the probability measure P; 3) as the supremum of Shannon's mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information. [ABSTRACT FROM AUTHOR]

I will briefly explain the definition and advantage of hybrid quantum information pro-cessing, which is hybridization of qubit and continuous-variable technologies. The final goal would be realization of universal gate sets both for qubit and continuous-variable quantum information processing with the hybrid technologies. For that purpose, qubit teleportation with a continuous-variable teleporter is one of the most important ingredients. [ABSTRACT FROM AUTHOR]

A direct evidence for Time Reversal Violation (TRV) means an experiment that, considered by itself, clearly shows TRV independent of, and unconnected to, the results for CP Violation. No existing result before the recent BABAR experiment with entangled neutral B mesons had demonstrated TRV in this sense. There is a unique solution for the test of TRV with unstable particles thanks to the Einstein-Podolsky-Rosen (EPR) Entanglement between the two neutral mesons in B, and ø, Factories. The two quantum effects of the decays as filtering measurements of the meson states and the transfer of information of the first decay to the still living partner allow performing a genuine TRV asymmetry with the exchange of "in" and "out" states. With four independent TRV asymmetries, BABAR observes a large deviation of T-invariance with a statistical significance of 14 standard deviations, far more than needed to declare the result as a discovery. This is the first direct observation of TRV in the time evolution of any system. The perspectives for future additional studies of TRV are discussed. [ABSTRACT FROM AUTHOR]

We calculate the Wigner (quasi)probability distribution function of the quantum optical elliptical vortex (QEV) generated by coupling squeezed vacuum states of two modes. The coupling between the two modes is performed by using beam splitter (BS) or a dual channel directional coupler (DCDC). The quantum interference due to coupling between the two modes promises the generation of controlled entanglement for quantum computation and quantum tomography. We compute the entanglement of such QEV formed by non-classical radiation field, using Wigner function. We report a critical squeezing parameter above which the entanglement is less for higher vorticity, which is counter intuitive. [ABSTRACT FROM AUTHOR]

Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots. [ABSTRACT FROM AUTHOR]

There are two powerful arguments against the possibility of extending quantum mechanics (QM) into a more fundamental theory yielding a deterministic description of nature. One is the experimental violation of Bell inequalities, which discards local hidden-variable theories as a possible extension to QM. The other is the Kochen-Specker (KS) theorem, which stresses the incompatibility of QM with a larger class of hidden-variable theories, known as noncontextual hidden-variable theories. We performed experiments with neutron interferometer, which exploits spin-path entanglements in single neutrons. A Bell-like state is generated to demonstrate a violation of the Bell-like inequality and phenomena in accordance with KS theorem: both experiments study quantum contextuality and show clear evidence of the incompatibility of noncontextual hidden variable theories with QM. The value S=2.202±0.007≰2 is obtained in the new measurement of the Bell-like inequality, which shows a larger violation than the previous measurement. For the study of KS theorem, the obtained violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories. [ABSTRACT FROM AUTHOR]

We study the exact solution of the lambda, vee and cascade type of three-level system with distinct Hamiltonian for each configuration expressed in the SU (3) basis. The semiclassical models are solved by solving respective Bloch equation and the existence of distinct non-linear constants are discussed which are different for different configuration. Apart from proposing a qutrit wave function, the atom-field entanglement is studied for the quantized three-level systems using the Phoenix-Knight formalism and corresponding population inversion are compared. [ABSTRACT FROM AUTHOR]

In this paper several non-classical properties are described such as the entanglement of bipartite system in the multimode cavities, described by the Jaynes-Cummings as well as the Tavis-Cummings model. The modes are described quantum mechanically, which helps to bring out the non-classical features emerging from the interaction of atoms with the cavity modes. Effects such as the growth of the magnitude of atomic entanglement with the increase of the cavity photon number, arising out of the intensity dependent atom-cavity coupling lead to interesting dissimilarities from the case of entanglement generated by the standard Jaynes-Cummings interaction. The dynamics of a single Rydberg atom in an n-mode cavity are also described by oscillations at the rate of the interaction strength of the atom-field interaction, Finally, we investigate the entanglement dynamics in the presence of cavity dissipation under single mode Tavis-Cummings interaction. The atom-photon interactions and the generation of entanglement mediated through them are expected to play an important role in possible future practical realizations in the field of quantum communications for various atom-photon interaction models considered under single or multimode cavity. [ABSTRACT FROM AUTHOR]

We show that long-distance steady-state quantum correlations (entanglement) between pairs of cavity-atom systems in an array of lossy and driven coupled resonators can be established and controlled. The maximal of entanglement for any pair is achieved when their corresponding direct coupling is much smaller than their individual couplings to the third party. This effect is reminiscent of the coherent trapping of the ?--type three-level atoms using two classical coherent fields. Different geometries for coherent control are considered. For finite temperature, the steady state of the coupled lossy atomcavity arrays with driving fields is in general not a thermal state. Using an appropriate distance measure for quantum states, we find that the change rate of the degree of thermalization with respect to the driving strength is consistent with the entanglement of the system. [ABSTRACT FROM AUTHOR]

In this work we examine the possibilities of converting quantum optical nonclassicality into entanglement in multimode under the action of classicality preserving devices such as beamsplitters. While the single mode case is amenable to a complete analysis, non availability of certain crucial results in the classical theory of moments in the multimode situations forces us to treat these cases with lesser degree of generality by taking recourse to the familiar Mandel matrix and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test which, if successful, simultaneouly witnesses nonclassicality as well as NPT entanglement. We develop a test for NPT entanglement after beamsplitter action on a nonclassical state, designed in such a way that it remains 'close' to that for nonclassicality. In the same spirit we analyse the result of three-mode 'beamsplitter' action after coupling to an ancilla in the Fock ground state. The concept of genuine tripartite entanglement and scalar measures of nonclassicality at the Mandel level for two mode systems are discussed and illustrated with the help of several examples. [ABSTRACT FROM AUTHOR]

For multimode radiation fields, the well known concept of nonclassicality is a prerequisite for entanglement. For single mode radiation fields, where entanglement is not meaningful, we study the possibilities of conversion of nonclassicality to entanglement after action by passive classicality preserving devices like beamsplitters. The theorems provided by the classical theory of moments play a key role in these considerations and lead to a complete answer to the problem. [ABSTRACT FROM AUTHOR]

The paper is to demonstrate that Informatics (as a discipline that is much deeper in fundamentals and broader in scope than so-called Computer science) and Physics are two disciplines that, in their fundamentals, have very similar goals, and their foundational structures as well as methodologies influence much each other - what has already been reflected in such slogans as Information is physical, Physics is informational and It from bit/qubit of Landauer and Wheeler/Deutsch. The discovery that information processing is inherent in the processes of nature and the discovery of such powerful information processing and transmission resources as entanglement and non-locality have much contributed to the understanding that much broader and deeper view of Informatics is needed and that from the development of such a new perception of Informatics both Physics and Informatics are much to profit. Mutual impacts of Physics and Informatics are illustrated bellow in several case studies. [ABSTRACT FROM AUTHOR]

We illustrate a procedure to generate a bipartite, entangled compass state, which shows sub-Planck structure. The proposed method uses the interaction of a standing wave laser field, with two, two-level atoms and relies on the ability of this system to choose certain mesoscopic bipartite states to couple with the internal degrees of freedom. An appropriate measurement on the internal degrees of freedom then leads to the entangled state, which shows sub-Planck structures, desired for quantum metrology. [ABSTRACT FROM AUTHOR]

The significance of sub-Planck structures in relation to quantum metrology is explored, in close contact with experimental setups. It is shown that an entangled cat state can enhance the accuracy of parameter estimations. The possibilty of generating this state, in dissipative systems has also been demonstrated. Thereafter, the quantum Cramer-Rao bound for phase estimation through a pair coherent state is calculated, which achieves the maximum possible resolution in an interferometer. [ABSTRACT FROM AUTHOR]

The non-locality of entangled systems provides more evidence that the spatial continuum of quantum particles is not classical. We assume that physical quantities take Dedekind real numbers in a topos for their numerical values. This means that the quantum spatial continuum is isomorphic to RD(EJ(M))³, where RD(EJ(M)) the sheaf of Dedekind real numbers in the topos Shv(EJ(M) of sheaves on the state space of the quantum system. In such a continuum, a single particle can have a quantum trajectory which passes through two classically separated slits and two particles in an entangled condition stay close to each other in their quantum space and hence Einstein locality is retained. [ABSTRACT FROM AUTHOR]

75 years after the term "entanglement" was coined to a peculiar feature inherent to quantum systems, the connection between quantum and classical mechanics remains an open problem. Drawing on recent results obtained in semiclassical systems, we discuss here the fate of entanglement in a closed system as Planck's constant becomes vanishingly small. In that case the generation of entanglement in a quantum system is perfectly reproduced by properly defined correlations of the corresponding classical system. We speculate on what these results could imply regarding the status of entanglement and of the ensuing quantum correlations. [ABSTRACT FROM AUTHOR]

The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern scientific thought. There are two kinds of statements about the world: those made from inside the world, and those from outside. The conflict between contradictory statements which both appear to be true can be resolved by recognising that they are made in different perspectives. Probability, in an objective sense, belongs in the internal perspective, and to statements in the future tense. Such statements obey a many-valued logic, in which the truth values are identified as probabilities. [ABSTRACT FROM AUTHOR]

Relativistic quantum information (RQI) is an emerging field of research dedicated to investigating quantum information protocols in a relativistic setting. Such models may give us clues about what sort of features a proper theory of quantum gravity ought to have. In this paper, we consider what happens to a quantum circuit operating in a curved spacetime background. We model the circuit using quantum optics in a Schwarzchild metric, with qubits constructed from single photons. The result is compared to an alternative model using ‘event operators’ in place of regular quantum optics. In this new model, field operators acting at different events in the photon’s history are made to commute with each other; a requirement that has elsewhere been shown to remove paradoxes from situations where closed time-like curves are involved. Our comparison of the models reveals that the event operator model is inherently non-linear, although it gives the same predictions as normal quantum optics in most cases. [ABSTRACT FROM AUTHOR]

We discuss how the entanglement properties of a multipartite pure state can be described by extending conventional matrix theory to the hypermatrix formed by the coefficients of the state with respect to a product basis. In particular, we show that the geometric measure of entanglement is given by an analogue of the largest singular value of a matrix. [ABSTRACT FROM AUTHOR]

I introduce a trigonometry to accompany the geometry of quantum states. This trigonometry is based upon my noncommutative operator trigonometry in which central entities are antieigen-values, antieigenvectors, and operator turning angles. The outcome of this paper is new understandings from this trigonometric viewpoint of important quantum state properties of entanglement, entropy, Bloch spheres, disentanglement, decoherence, Schmidt angles, quantum channels, and orbit stratification. [ABSTRACT FROM AUTHOR]

Using a three-particle entangled system (triple) of photons, it is possible in principle to transmit signals faster than the speed of light from sender to receiver in the following manner: First, let there be an emitter of triples between sender and receiver. For every triple, photons 1 and 2 are sent to the receiver and 3, to the sender. The sender is given the choice of whether to (a) measure polarization of photon 3 or (b) destroy such information. On the other hand, the receiver measures photon correlation vs. relative polarization angle between photons 1 and 2. These correlation statistics depend on whether photon 3 polarization was (a) measured or (b) destroyed. Since this dependence is nonlocal, it is a basis for superluminal i.e. faster-than-light communication. [ABSTRACT FROM AUTHOR]

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a κ-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibniz rule. We explore the richer structure of the κ-Fock space and point out possible physical consequences of the deformation. [ABSTRACT FROM AUTHOR]

The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the constraint and Hamiltonian operators. Matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole. Matter fields alone are an open system with a non-unitary evolution. However, if there is a successful theory of quantum gravity, there is no information loss. [ABSTRACT FROM AUTHOR]

The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well. [ABSTRACT FROM AUTHOR]

In this article we discuss our two recent proposals on producing and detecting of entangled states in quantum conductors. First we analyze a setup where two electrons are scattered on a quantum dot with Coulomb repulsion and became orbitally entangled. Second, for identical noninteracting particles we suggest an operating scheme for the deliberate generation of spin-entangled electron pairs in a normal-metal mesoscopic structure with a fork geometry. The spin-entangled pair is created through a post-selection in the two branches of the fork. We also make comments on different ways of producing and quantifying the degree of entanglement. [ABSTRACT FROM AUTHOR]

Entanglement entropy is a measure of quantum correlations between separate parts of a many-body system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the Full Counting Statistics description of electron transport was established for noninteracting fermion systems. Using this relation, which is of a completely general character, we discuss how the entanglement entropy can be directly measured by detecting current fluctuations in a driven quantum system such as quantum point contact. [ABSTRACT FROM AUTHOR]

We explore possible characterisations of entanglement classes which may be interpreted as gates acting on globally distributed systems. The cyclic nature of a selection of entanglement gates, primitives, is explored commencing with gates for generating Bell, GHZ and W states. [ABSTRACT FROM AUTHOR]

We provide a simple model to study memory effects in a lossy bosonic quantum channel over arbitrary number of uses. The noise correlation among different uses is introduced by contiguous modes interactions which results in an exponential decay of the correlations over channel uses (modes). This model allows us to characterize the asymptotic behavior of the channel for classical information transmission. This submission is based on the work [1]. [ABSTRACT FROM AUTHOR]

We experimentally demonstrate distillation of continuous variable entangled light that has undergone non-Gaussian attenuation loss. The continuous variable entanglement is generated with optical fibers and sent through a lossy channel, where the transmission is varying in time. By employing simple linear optical components, a measurement induced operation and classical communication, we demonstrate that the entanglement is probabilistically increased. [ABSTRACT FROM AUTHOR]

We show that a local control of the effective magnetic field in a spin chain allows for an efficient storage of bipartite entanglement and for its transmission “on demand” towards a selected receiving site. [ABSTRACT FROM AUTHOR]

We discuss different levels of quantum correlations in the continuous variable regime and illustrate them by means of experimental results with an optical parametric oscillators. More specifically, we report the first experimental generation of bright frequency-degenerate EPR beams with a type II OPO. Degeneracy is obtained by introducing a birefringent plate inside the cavity, resulting in phase locking. Correlation is characterized by homodyne detection. [ABSTRACT FROM AUTHOR]

We investigate the quantum features, entanglement and resilience to losses, of multiphoton fields generated by optical amplification of photon entangled states. We first report the realization of a class of Microscopic-Macroscopic entangled states of more than 5×104 photons, based on parametric amplification of single-photon and two-photons states. A non-locality CHSH-type test has been performed on this system. Then, we apply a decoherence model to this Micro-Macroscopic entangled state, showing their high resilience to photon-loss. The theoretical results are in full agreement with many experimental observations. [ABSTRACT FROM AUTHOR]

We report on a measurement of entanglement in the time domain. The entanglement is examined by the Duan-Simon criteria. We obtained Duan-Simon criteria of Δ2(x1-x2)+Δ2(p1+p2) = 1.4<2 without optimal gain and Δ2(x1-x2)+Δ2(p1+p2) = 1.2<2 with optimal gain, respectively. This opens the way to realize both efficient and truly causal EPR paradox. [ABSTRACT FROM AUTHOR]

Parametric downconversion (PDC) is a popular technique to produce twin beams of photons that are entangled in multiple degrees of freedom. The generated states form the basis for numerous applications that require entanglement. An exact quantification of this resource is therefore essential, for instance for quantum cryptography that relies on a complete knowledge of the correlation contained in the state. While the determination of an entanglement monotone for the PDC process is only possible analytically in special cases, an exact calculation must usually be performed numerically. Recent work by Mikhailova et al. [2] analyses a certain class of PDC states for which the concurrence entanglement measure can be obtained by an analytical approximation. In this contribution, we analyse the validity of the approximation by comparison with exact numerical methods. [ABSTRACT FROM AUTHOR]

Developments in quantum information science rely critically on entanglement, as its distribution between different parties enables quantum communication protocols, such as quantum key distribution or teleportation. This talk focused on two different ways to generate heralded entanglement between matter systems, a critical requirement for scalable quantum networking. [ABSTRACT FROM AUTHOR]

A protocol is proposed robust against the theft of smart cards for authentication quantum keys. The protocol also prevents the leakage of secret information of a certification agent. [ABSTRACT FROM AUTHOR]

The Feynman propagator has nonzero components outside of the light cone. As a result, entanglement and mutual information can be generated between two space-like separated points. Two possible interpretations of these effects are discussed. [ABSTRACT FROM AUTHOR]

By combining a measure of total correlations, mutual information, and the notion of broadcast —i.e. generally non-factorized— copies of states of distributed systems, we are able to characterize in a single framework different levels of quantumness of correlations, corresponding to the classification of strictly classical, separable, and entangled states. We find that the broadcast regularization of mutual information —defined as the minimal per-copy mutual information between parties, when they share an infinite amount of broadcast copies— besides having by construction an appealing interpretation, satisfies many of the properties of an entanglement measure. In particular, it vanishes for separable states while it is strictly positive for all entangled states. The latter fact may be considered a signature of monogamy of entangled correlations. [ABSTRACT FROM AUTHOR]

We define partial K-way negativities for N-qubit states. For the states in canonical form, global and K-way negativities measure the entanglement of the state. [ABSTRACT FROM AUTHOR]

A Bell test is performed on a Micro-Macroscopic photon system obtained by parametric amplification of a spin-1 entangled photon state. The optical parametric amplification leads to the creation of a Micro-Macroscopic entangled system consisting of N≃3.5×104. The performed Bell’s inequality non locality test involves the adoption of a positive operator valued measurement (POVM) strategy for a sharper identification of the amplified states. This is obtained through a local filtering technique and the experimental data are found to violate the Bell’s inequality albeit with a loophole similar to the detection efficiency one in photon counting experiments. [ABSTRACT FROM AUTHOR]

Motivated by the fact that random quantum states are generic, i. e., that they occur as eigenvectors or during time evolution of sufficiently complex quantum system, we are going to address three questions: (i) what is the entanglement content of random quantum states, (ii) how can we efficiently generate them, and (iii) how come that there is apparently no entanglement in macroscopic world. To explain the later we will use properties of random quantum states. To answer the first question we are going to calculate average values of all Schmidt coefficient and to address the second one we are going to explicitly calculate convergence times of various random protocols. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of a system consisting of a Cooper-pair box and two superconducting transmission line resonators. There exist both linear and nonlinear interactions in such a system. We show that single-photon entanglement state can be generated in a simple way in the linear interaction regime. In nonlinear interaction regime, we derive the Hamiltonian of degenerate three-wave mixing and propose a scheme for generating squeezed state of microwave using the three-wave mixing in solid state circuits. In the following, we design a system for generating squeezed states of nanamechanical resonator. [ABSTRACT FROM AUTHOR]

We discuss past, present, and future entropy challenges due to the fundamental questions that arise when the Second Law of Thermodynamics is confronted with Classical and Quantum Mechanics. [ABSTRACT FROM AUTHOR]

These lecture notes give an introduction to quantum magnetism. We start by a discussion of paramagnetism and the Weiss meanfield theory applied to the Ising model. In the following sections, we turn to the fully quantum-mechanical Heisenberg Hamiltonian. First, we consider the limit of small clusters whose properties we analyze via exact diagonalization. Bulk quantum magnets are then within the framework of the linear spinwave theory. A short discussion of Monte Carlo techniques follows. Finally, we discuss aspects of entanglement in quantum spin systems. [ABSTRACT FROM AUTHOR]

This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions. [ABSTRACT FROM AUTHOR]

The interaction of two electrons in a double quantum dot structure with an electromagnetic field is studied. Using proper approximations we obtain analytical solutions for the time evolution of the probabilities in the several quantum states and present conditions for the creation of maximally entangled two-electron states. [ABSTRACT FROM AUTHOR]

We analyse the commonly used adiabatic techniques in the atom-cavity field interaction to controllably entangle two distant atoms trapped inside a single-mode optical cavity. Two techniques are considered: the first involves a highly detuned cavity from the atomic transition frequencies, and the second involves a near resonant but strongly damped cavity. We show that both, the detuning and the cavity damping are needed to obtain the master equation of the collectively interacting atoms. We analyse the feasibility of the adiabatic techniques in creation of a long living entanglement and find that the cavity damping is more robust for generation of a stationary entanglement between the atoms. The dependence of the stationary entanglement on number of excitations in the system and strengths of the couplings of the atoms to the cavity mode is also discussed. [ABSTRACT FROM AUTHOR]

We present details on a physical realization, in a many-body Hamiltonian system, of the abstract probabilistic structure recently exhibited by Gell-Mann, Sato and one of us (C.T.), that the nonadditive entropy Sq = k[1-Trρq]/[q-1] (ρ≡density matrix; S1 = -kTrρ ln ρ) can conform, for an anomalous value of q (i.e., q≠1), to the classical thermodynamical requirement for the entropy to be extensive. Moreover, we find that the entropic index q provides a tool to characterize both universal and nonuniversal aspects in quantum phase transitions (e.g., for a L-sized block of the Ising ferromagnetic chain at its T = 0 critical transverse field, we obtain limL→∞S37-6(L)/L = 3.56±0.03). The present results suggest a new and powerful approach to measure entanglement in quantum many-body systems. At the light of these results, and similar ones for a d = 2 Bosonic system discussed by us elsewhere, we conjecture that, for blocks of linear size L of a large class of Fermionic and Bosonic d-dimensional many-body Hamiltonians with short-range interaction at T = 0, we have that the additive entropy S1(L)∝[Ld-1-1]/(d-1) (i.e., ln L for d = 1, and Ld-1 for d>1), hence it is not extensive, whereas, for anomalous values of the index q, we have that the nonadditive entropy Sq(L)∝Ld(∀d), i.e., it is extensive. The present discussion neatly illustrates that entropic additivity and entropic extensivity are quite different properties, even if they essentially coincide in the presence of short-range correlations. [ABSTRACT FROM AUTHOR]

Review of the probability representation of quantum mechanics, in which a fair probability distribution is used instead of the density matrix or wave function to describe quantum states is presented. Bell inequalities are formulated as properties of joint probability distributions describing the states of multipartite spin systems in the probability representation. Probability distributions depending on extra parameters are discussed in the connection with problems of classical and quantum statistical mechanics, where these distributions can be considered in the context of non-Kolmogorov probability theory. [ABSTRACT FROM AUTHOR]

We argue that quantum mechanics, in reality, respects the principles of a macroscopic realism (PMRs). The current quantum theory to tell us that “...the state of a system can be instantaneously changed by a distant measurement...” is not a physical one. Its key statements—that the violation of Bell's inequality in the EPR-Bell experiments verifies nonlocality, and nonlocal correlations respect special relativity—are false. Both the EPR-Bell experiments and theorems to support the “non-signalling principle” resort to the quantum mechanical averaging rule which is inapplicable to Cat states because such averaging violates the correspondence principle (CP). The main idea of the paper is exemplified by our model of a one-dimensional completed scattering. [ABSTRACT FROM AUTHOR]