# States used in lossless quantum compression?

1. In example they represented $$|a\rangle = \dfrac{1}{\sqrt{15}}|00\rangle + \dfrac{1}{\sqrt{15}}|10\rangle +\dfrac{2}{\sqrt{15}}|01\rangle + \dfrac{1}{\sqrt{15}}|11\rangle$$. How can they call this a quantum state given that the sum of square magnitudes of the amplitudes is not equal to one?
2. If they are compressing kets ($$|10\rangle$$ to $$|1\rangle$$) then what is the point of the amplitudes $$\dfrac{1}{\sqrt{15}}$$?
• I'd add that the author says the state $|a\rangle$ is a mixed state. Weird. – kludg Apr 19 at 3:34