  In a previous work we constructed a new kind of moduli background space by
identifying regions of space-time where an observation of space-time is
implied. We called it Observation Modular space (OM-space). Quantum Mechanics
(QM) on this moduli space gets mapped into a very rich and highly non trivial
dual Number Theory which we call Observation Modular Quantum Mechanics (OM-QM).
In this work we extend the scope of this modularization to include observations
of quantum states. We call the resulting extended space Observation Modular
Riemann-Hilbert space (OM-RH space). It has the mathematical structure of a
Riemann Surface. We find the OM-QM analogue of quantum base states and mixed
states. This allows us to find the OM-QM analogues to the quantum State
Reduction postulate and the Born rule. The OM-QM analog to quantum state
collapse turns out to be totally deterministic and unitary in OM-RH space. It
is shown to be equivalent to an Elliptic Curve Encryption-decryption protocol.
Finally we obtain the OM-QM analog of entangled quantum states. As an example
we apply this to the OM-QM interpretation of the EPR experiment.
