Quantum Kolmogorov Complexity and Quantum Key Distribution Export

@article{citeulike:3563659, abstract = {We discuss BB84 quantum key distribution protocol in light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The theory regards a program length necessary to describe an object, Kolmogorov complexity, as the most fundamental quantity. Recently, its quantum versions were proposed by a several researchers. We employ a definition of quantum Kolmogorov complexity given by Vitanyi. A goal of the quantum key distribution is to distribute a random binary sequence only between legitimate users. In the context of quantum algorithmic complexity, a security criterion is formulated with the quantum Kolmogorov complexity. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve in a probability exponentially close to 1.}, archivePrefix = {arXiv}, author = {Miyadera, Takayuki and Imai, Hideki}, citeulike-article-id = {3563659}, citeulike-linkout-0 = {http://arxiv.org/abs/0811.2460}, citeulike-linkout-1 = {http://arxiv.org/pdf/0811.2460}, day = {15}, eprint = {0811.2460}, month = {Nov}, posted-at = {2008-11-18 02:33:44}, priority = {2}, title = {Quantum Kolmogorov Complexity and Quantum Key Distribution}, url = {http://arxiv.org/abs/0811.2460}, year = {2008} }

TY - JOUR ID - citeulike:3563659 L3 - citeulike-article-id:3563659 N2 - We discuss BB84 quantum key distribution protocol in light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The theory regards a program length necessary to describe an object, Kolmogorov complexity, as the most fundamental quantity. Recently, its quantum versions were proposed by a several researchers. We employ a definition of quantum Kolmogorov complexity given by Vitanyi. A goal of the quantum key distribution is to distribute a random binary sequence only between legitimate users. In the context of quantum algorithmic complexity, a security criterion is formulated with the quantum Kolmogorov complexity. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve in a probability exponentially close to 1. TI - Quantum Kolmogorov Complexity and Quantum Key Distribution AU - Miyadera, Takayuki AU - Imai, Hideki PY - 2008/Nov/15/ UR - http://arxiv.org/abs/0811.2460 ER -