  It is pointed out that every mixed state statistical operator is, up to a
normalization constant, a super state vector in the Hilbert space of linear
Hilbert-Schmidt operators acting in the state space of the quantum system.
Hence, the well understood Schmidt canonical expansion of ordinary state
vectors can be carried over to mixed states. In particular, it can be utilized
for evaluating all the twins, i. e., the opposite-subsystem observables the
measurement of one of which is, on account of entanglement, ipso facto also a
measurement of the other. This is illustrated in full detail in the case of the
Horodecki two spin-one-half-particle states with maximally disordered
subsystems.

Quantum Physics