Quantum Kolmogorov complexity and its applications

Details Quantum Kolmogorov complexity and its applications Quantum Kolmogorov complexity and its applications

2006-10-13

arxiv.org/abs/quant-ph/0610109v1

Physics

Quantum Physics

12 pages, no figures

Scientific paper

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

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