Abstract. The challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states (density operators). A family of tripartite states satisfying equality is derived. †
The many-identical-particle quantum correlations are revisited utilizing the machinery of basic group theory, especially that of the group of permutations. It is done with the purpose to obtain precise definitions of effective distinct particles, and of the limitations involved. Namely, certain restrictions allow one to distinguish identical particles in the general case of N of them, and of J clusters of effectively distinct identical particles, where N and J are arbitrary integers (but 2 ≤ J ≤ N ). Mutually orthogonal, single-particle distinguishing projectors (events or properties), J of them, are the backbone of the construction. The general results are exemplified by local quantum mechanics, and by the case of nucleons. The former example suits laboratory experiments, and a critical view of it is presented.
Abstract. Twin observables, i.e. opposite subsystem observables A + and A − that are indistinguishable in measurement in a given mixed or pure state ρ, are investigated in detail algebraicly and geometrically. It is shown that there is a farreaching correspondence between the detectable (in ρ) spectral entities of the two operators. Twin observables are state-dependently quantum-logically equivalent, and direct subsystem measurement of one of them ipso facto gives rise to the indirect (i.e. distant) measurement of the other. Existence of nontrivial twins requires singularity of ρ. Systems in thermodynamic equilibrium do not admit subsystem twins. These observables may enable one to simplify the matrix representing ρ.
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