Mixed-state twin observables

Twin observables are opposite subsystem observables A(+) and A(-) if they a re indistinguishable in measurement in a given mixed or pure state rho in t he sense that the measurement of one amounts to the same as the measurement of the other (direct measurement and so-called distant measurement, respec tively). It is pointed out that twin observables may reveal quantum correla tions that give rise to the disappearance of interference in the two-slit e xperiment. Twin observables in general states are investigated in detail al gebraically and geometrically.;It is shown that there is a far-reaching cor respondence between the detectable (in rho) spectral entities of the two op erators. Twin observables are state-dependently quantum-logically equivalen t, and the direct subsystem measurement of one of them ipso facto gives ris e to the indirect (i.e. distant) measurement of the other. Existence of non trivial twins requires a singularity of rho. Systems in thermodynamic equil ibrium do not admit subsystem twins. These observables may enable one to si mplify the matrix representing rho.