John Preskill

John Watrous

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Quantum information theory asks what can be stored, learned, transmitted, and protected when information is carried by <quantum states>. Its basic objects are <density operators>, <quantum measurements>, and <quantum channels>; its resources include <qubits>, <entanglement>, and <classical communication>. Specifying the task matters: preserving an unknown <quantum state>, recovering a classical <bit>, and estimating a <probability amplitude> are different demands on the same physical system.

A particularly beautiful feature is that knowing the whole need not mean knowing its parts. A <Bell state> is a completely specified <pure state>, yet either <qubit> alone has a maximally uncertain <reduced density matrix>. Conversely, two systems can share perfectly matching measurement records without <entanglement>. The worked <Bell correlations versus a classical mixture> comparison separates these possibilities using only two choices of <Pauli measurement>.

This viewpoint makes limitations useful design rules. <Schumacher compression> asks how much quantum memory a source needs; <Holevo's theorem> limits the classical information extractable from an encoding; <quantum error correction> protects states against noise. <Quantum teleportation> uses shared <entanglement> and <classical communication> to transfer an unknown state. Its resource accounting respects both <quantum no-signalling> and the <no-cloning theorem>.


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