All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

本文对国际科学计量学杂志《Ｓｃｉｅｎｔｏｍｅｔｒｉｃｓ》１９７９－１９９１年的研究论文内容、栏目、作者及国别和编委及国别作了计量分析，揭示出科学计量学研究的重点、活动的中心及发展趋势，说明了学科带头人在发展科学计量学这门新兴学科中的作用。

国际刊物《Scientometrics》文献计量研究

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

/pdf/the-classical-quantum-boundary-for-correlations-discord-and-3rixt19msw.pdf

The classical-quantum boundary for correlations: Discord and related measures

a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)

Geometry of Quantum States: Frontmatter

Quantum theory: Concepts and methods

Slater P. B. (1976) A hierarchical regionalization of Japanese prefectures using 1972 interprefectural migration flows, Reg. Studies 10, 123–132. A methodology for utilizing an interregional transaction flow table to construct a hierarchical system of regions is presented. The square matrix is first adjusted by a biproportional procedure to possess uniform row and column sums. A series of increasingly sparse digraphs can then be associated with the table by raising threshold levels which are used to convert it into (0, 1) matrices. The strong components of these digraphs (Boolean adjacency matrices) can be hierarchically arranged. 1972 Japanese interprefectural migration data are examined in this manner. Several officially recognized regions (chiho)—Shikoku, Chugoku, Tohoku, and Kyushu—are readily distinguished, since they correspond to strong components which are stable over a wide range of thresholds. The chiho of Kanto, Chubu and Kinki are not identified, however. The Seto-Uchi area, San-in and several...

A hierarchical regionalization of Japanese prefectures using 1972 interprefectural migration flows

Zyczkowski, Horodecki, Sanpera and Lewenstein (ZHSL) recently proposed a `natural measure' on the N-dimensional quantum systems, but expressed surprise when it led them to conclude that for N = 2 × 2, disentangled (separable) systems are more probable (0.632±0.002) in nature than entangled ones. We contend, however, that ZHSL's (rejected) intuition has, in fact, a sound theoretical basis, and that the a priori probability of disentangled 2 × 2 systems should more properly be viewed as (considerably) less than 0.5. We arrive at this conclusion in two quite distinct ways, the first based on classical and the second, quantum considerations. Both approaches, however, replace (in whole or part) the ZHSL (product) measure by ones based on the volume elements of monotone metrics, which in the classical case amounts to adopting the Jeffreys' prior of Bayesian theory. Only the quantum-theoretic analysis - which yields the smallest probabilities of disentanglement - uses the minimum number of parameters possible, that is N2-1, as opposed to N2+N-1 (although this `over-parametrization', as recently indicated by Byrd, should be avoidable). However, despite substantial computation, we are not able to obtain precise estimates of these probabilities and the need for additional (possibly supercomputer) analyses is indicated - particularly so for higher-dimensional quantum systems (such as the 2 × 3 ones, which we also study here).

A priori probabilities of separable quantum states

A LONG-RANGE STUDY IS BEING UNDERTAKEN OF INDIRECT IMPACTS OF THE LINDENWOLD TRANSIT LINE. PHASE ONE, OF WHICH THIS IS THE SUMMARY REPORT, SOUGHT TO DETERMINE WHETHER APPROVAL, CONSTRUCTION, AND OPERATION OF THE LINE HAVE HAS AN EFFECT ON RESIDENTIAL PROPERTY VALUES AND LAND DEVELOPMENT. (OPERATION OF THE LINE BETWEEN PHILADELPHIA AND THE NEW JERSEY SUBURBS BEGAN IN FEBRUARY 1969.) THE MAJOR CHAPTER HEADINGS ARE: THE HIGH-SPEED LINE AND ITS ENVIRONMENT, A SAVINGS MODEL OF PROPERTY VALUE IMPACTS, REAL ESTATE TRANSACTIONS AND PROPERTY CHARACTERISTICS DATA, DETECTION OF TRANSPORTATION IMPACTS THROUGH THE DECOMPOSITION OF RESIDENTIAL SALES PRICE DATA, STATISTICAL ANALYSES OF TRANSPORTATION IMPACT ON RESIDENTIAL SALES PRICES, CASE STUDIES OF LAND DEVELOPMENT POLICIES OF MUNICIPALITIES ADJACENT TO OUTLYING STATIONS, AND IMPACT OF GROWTH ON PUBLIC FINANCE. THE PRINCIPAL CONCLUSIONS ARE: (1) THE HIGH- SPEED LINE DID HAVE A POSITIVE IMPACT ON RESIDENTIAL PROPERTY VALUES IN ITS SOUTH JERSEY MARKET AREA. (2) THIS IMPACT APPEARS TO AGREE WITH THE THEORY THAT TRAVEL COST TIME SAVINGS STEMMING FROM THE USE OF THE LINE ARE BEING REFLECTED IN THE PRICES OF RESIDENTIAL HOUSING. (3) IN ADDITION TO SPATIAL VARIATION, THE IMPACT VARIES WITH SOCIOECONOMIC GROUP AND IS MORE APPARENT IN LOWER AND MIDDLE INCOME AREAS THAN IN HIGHER INCOME AREAS. (4) THERE IS LITTLE EVIDENCE THAT ANTICIPATION OF THE OPENING OF THE LINE HAD AN IMPACT ON RESIDENTIAL SALES PRICES BEFORE THE LINE STARTED TO OPERATE. (5) SOME EVIDENCE WAS FOUND TO SUPPORT THE HYPOTHESIS THAT AT LEAST A PORTION OF THE IMPACT IN THE CORRIDOR IS A TRANSFER OF PROPERTY VALUES FROM NEARBY UNSERVED CORRIDORS.

Impact of rapid transit on suburban residential property values and land development

Internal migration tables can be employed to ascertain functional migration regions?collections of geographic units with relatively large intraregional flows and relatively small interregional movements. A two-stage algorithm that has been utilized to study tables for various nations is applied here to a 21 × 21 French matrix. In the first step, the square table is adjusted to possess uniform marginal (row and column) sums. The doubly standardized table obtained can be regarded as an asymmetric similarity matrix. It serves, in the second stage, as input to a hierarchical clustering procedure, based on the concep of the strong components of a directed graph. Region Parisienne and Centre are shown to have the broadest migration bases. Well-defined southern and northwestern regions are found.

Hierarchical Internal Migration Regions of France

https://arxiv.org/pdf/quant-ph/0308037.pdf

Paul B. Slater

Papers

A hierarchical regionalization of Japanese prefectures using 1972 interprefectural migration flows

A priori probabilities of separable quantum states

Impact of rapid transit on suburban residential property values and land development

Hierarchical Internal Migration Regions of France

Silver mean conjectures for 15-dimensional volumes and 14-dimensional hyperareas of the separable two-qubit systems