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

Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons

The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to be essential even in intergalactic space in restricting the observable properties by locally destroying the corresponding phase relations. The remaining coherence determines the ‘classical’ properties of the macroscopic systems. In this way local classical properties have their origin in the nonlocal character of quantum states.

The emergence of classical properties through interaction with the environment

(1963). Cybernetics, or Control and Communication in the Animal and the Machine. Technometrics: Vol. 5, No. 1, pp. 128-130.

Cybernetics, or Control and Communication in the Animal and the Machine

A quasidegenerate perturbation theory based on multiconfigurational self‐consistent‐field (MCSCF) reference functions is derived. The perturbation theory derived here is for multistate, where several MCSCF functions obtained by the state‐averaged MCSCF method are used as the reference and an effective Hamiltonian is constructed by perturbation calculation. The energies of states interested in are obtained simultaneously by diagonalization of the effective Hamiltonian. An explicit formula of the effective Hamiltonian through second order is derived as well as general formalism, and is applied to calculate potential curves of the system H2, Be–H2, CO, NO, BN, and LiF. The results agree well with those of full configuration interaction or multireference single and double excitation configuration interaction methods for both the ground and the excited states.

Quasidegenerate perturbation theory with multiconfigurational self‐consistent‐field reference functions

Chemistry, Quantum Mechanics and Reductionism

Relations between the simple form of MO-theory (two parameter theory) and the theory of spectra of graphs are investigated. By the use of some theorems of graph theory it is shown that the spectra of energy eigenvalues given by the simple MO-theory are determined besides of scale factors by the topology of the conjugated systems. Furthermore bond orders and charge orders are completely determined by the topology. A procedure for the calculation of the characteristic polynom and the characteristic vectors directly from the graph is given.

Zusammenhang von Graphentheorie und MO-Theorie von Molekeln mit Systemen konjugierter Bindungen

It is proposed to formulate any quantum mechanical perturbation theory in operator form and to take advantage of the fact that such a theory can be completely formulated in the domain of a Lie algebra. The concept of a T- operator is generalized and used to compose a solution of a complicated quantum mechanical problem from subproblems connected therein. (R.E.U.)

Generalized perturbation theory in operator form

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsacker [44]. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsacker developed Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position.

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Epistemic and Ontic Quantum Realities

It is a curious fact that our popular text books and most discussions of conceptual and philosophical problems of quantum mechanics are still based on the very first attempts to formalize this theory which have been worked out more than 50 years ago. These formulations of nonrelativistic quantum theory do, however, not represent the state of the art.

Hans Primas

Papers

Chemistry, Quantum Mechanics and Reductionism

Zusammenhang von Graphentheorie und MO-Theorie von Molekeln mit Systemen konjugierter Bindungen

Generalized perturbation theory in operator form

Epistemic and Ontic Quantum Realities

Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems