Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 32 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 34 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 60 / 1 / Solution

{title2=$\rho=\sum_xp_x|\psi_x\rangle\langle\psi_x|,\quad\rho^{(n)}=\rho^{\otimes n}$}

A pure-state source emits independent states from a fixed <quantum state ensemble>. Its average block <density operator> is the tensor power of the one-use average. Unassisted <reliable quantum source compression> preserves the emitted quantum states, rather than only their classical labels. <Schumacher compression> gives the optimum asymptotic qubit rate $S(\rho)$ for such a source, with every larger rate achievable. Nonorthogonal equally likely pure states need not have entropy one: their classical labels have entropy one but their average density operator can have lower <Von Neumann entropy>.

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 Incoming links: Memoryless quantum information source