Characterization and visualization of the state and entanglement of two spins

We characterize and classify the quantum states of a pair of Spin-1/2 parti cles in terms of the entanglement of the pair. We describe a general strate gy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available-a pair of spin-1/2 particles. The method is based on local unitary transformations. We give a set of six para meters that describe an arbitrary pure state of a pair of spins, one of whi ch is the entanglement of the pair. We discuss visual representations of th e state of this system, and propose a visualization using a Bloch sphere fo r each subsystem and a disc to record the 'shared' information.