  We consider a scenario where interacting electrons confined in quantum dots
(QDs) are either too close to be resolved, or we do not wish to apply
measurements that resolve them. Then the physical observable is an electron
spin only (one cannot unambiguously ascribe a spin to a QD) and the system
state is fully described by the spin-density matrix. Accounting for the spatial
degrees of freedom, we examine to what extent a Hamiltonian description of the
spin-only degrees of freedom is valid. We show that as long as there is no
coupling between singlet and triplet states this is indeed the case, but when
there is such a coupling there are open systems effects, i.e., the dynamics is
non-unitary even without interaction with a true bath. Our primary focus is an
investigation of non-unitary effects, based on exact master equations we derive
for the spin-density matrix in the Lindblad and time-convolutionless (TCL)
forms, and the implications for quantum computation. In particular, we
demonstrate that the Heisenberg interaction does not affect the unitary part
(apart from a Lamb shift) but does affect the non-unitary contributions to time
evolution of the spin-density matrix. In a sequel paper we present a detailed
analysis of an example system of two quantum dots, including spin-orbit
effects.
