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Pure vs Mixed States

Pure state#

The quantum state we referred to so far are what one calls pure states, and they are represented by a normalised vector in a complex Hilbert space. In the Dirac notation, they are described as a ket \(|v\rangle\) or a bra \(\langle v|\).

-

There is another way to describe the state of quantum system which can be generalised to mixed states (defined below), and the is through density operator. For a system in pure quantum state \(|v\rangle\), the density operator is defined as -$\( +

There is another way to describe the state of quantum system which can be generalised to mixed states (defined below), and the is through density operator. For a system in pure quantum state \(|v\rangle\), the density operator is defined as

+
+\[ {\Huge \rho = |v\rangle \langle v| } -\)$

+\]