QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

CATERINA E. MORA, HANS J. BRIEGEL, BARBARA KRAUS
2007 International Journal of Quantum Information  
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
more » ... ation 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. PACS numbers:
doi:10.1142/s0219749907003171 fatcat:27eptxbcxbblxh7kuybxeffyte