Editing Glossary (section)

===Density Matrix, Pure and Mixed states===
A density matrix is the matrix representation of a statistical state in quantum mechanics. This is a useful representation for mixed states. The mixed states are the states which cannot be described with a single vector $|\psi\rangle$ in Hilbert space. Instead, they are statistical mixture of several pure states. These states are also useful for describing the quantum state of a subsystem of a multi-party or larger quantum sysytem where the overall state can be shown as pure states. a density matrix in general can be shown as:<br/><br/>
<math>\rho = \sum_{i} p_i |\psi_i\rangle\langle\psi_i|</math><br/>
where <math>|\psi_i\rangle</math> are pure states and <math>p_i</math> are the relative probabilities. For a pure quantum state <math>|\psi\rangle</math> the density matrix representation will be:<br/>
<math>\rho = |\psi\rangle\langle\psi|</math>