Normally in an EPR experiment two measurements are performed on entangled particle pair. Only the particle pair is treated quantum mechanically and it is usually prepared in a state like $$ (\,\left|\uparrow \downarrow\right>+\left|\downarrow\uparrow\right>\,)/\sqrt{2} $$ In modern approaches to QM it is common to also treat the detectors as a part of the experiment that the rest of the experiment becomes entangled with. The measurement of the left spin in the parallel direction can then be represented by the transition $$ \left|0\right>\,(\,\left|\uparrow\downarrow\right>+\left|\downarrow\uparrow\right>\,)/\sqrt{2} \leadsto (\,\left|\uparrow\uparrow\downarrow\right>+\left|\downarrow\downarrow\uparrow\right>\,)/\sqrt{2}$$ where $\left|0\right>$ represents the ready state of the detector.
In a typical EPR experiment we would measure the right spin. If the measurement was again in the parallel direction this would determine the state of all of the components. In what sense is the entanglementafter the first measurement monogamous? Is there an error in the above description?
