This paper is dedicated to Sylvia Pulmannová, in appreciation of her scientific accomplishments, and also for the enjoyment and privilege to be co-author in some of her research articles, as well as meeting her personally. One of the most remarkable impressions on me (K.S.) was her humbleness as a person and colleague, accompanied by her extreme professional skills in mathematics, logics and physics. (Communicated by Anatolij Dvurečenskij) ABSTRACT. Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite quantized systems can be partitioned, and their observables grouped and redefined into condensed correlations. c○2010

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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper-) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the self-contradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.

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A glance at singlet states and four-partite correlations

Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite quantized systems can be partitioned, and their observables grouped and redefined into condensed correlations. PACS numbers: 03.67.Hk,03.65.Ud

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.

The group theoretical aspect of the description of passive lossless optical four-ports (beam splitters) is revisited. It is shown through an example, that this approach can be useful in understanding interferometric schemes where a low number of photons interfere. The formalism is extended to passive lossless optical six-ports, their SU(3)-theory is outlined. 1