Algorithmic complexity of quantum states

Details Algorithmic complexity of quantum states Algorithmic complexity of quantum states

2004-12-22

arxiv.org/abs/quant-ph/0412172v1

Physics

Quantum Physics

24 pages, no figures

Scientific paper

In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive idea of complexity as a measure of ``how difficult'' it is to prepare a state. We apply this definition to give an upper bound on the algorithmic complexity of a number of states.

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