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John Preskill's quantum computation notes develop the distinction between a quantum state ray, a normalized wave function, and a density operator. This makes a practical difference for a subsystem of an entangled state: its predictions are described by a reduced density operator obtained with the partial trace, even when the joint quantum state is pure. His discussion also shows why different statistical preparations can give the same density operator and therefore identical predictions for measurements confined to that subsystem.^[ref]

A theoretical physicist working on quantum information theory.^[ref]

Homepage: www.preskill.caltech.edu/

A computer scientist working on quantum information theory.^[ref]

Institutional profile: uwaterloo.ca/institute-for-quantum-computing/profiles/john-watrous

Peter Shor is a mathematician whose research includes quantum computing, quantum information theory, algorithms and computational geometry.^[ref] His quantum algorithms for integer factorization and discrete logarithms require a number of steps polynomial in the number of input digits. They made the distinction between classical and quantum computational resources concrete for problems used in cryptography.^[ref]

Quantum information science studies the storage, processing and transmission of quantum information, including the physical implementation of the tasks described by quantum information theory.