منابع مشابه
0 Quantum Algorithmic Entropy
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (" universal probability ") as a starting point, and define complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately , a quantum state is simple if it is within a small distance from a low-dim...
متن کاملQuantum Algorithmic Entropy
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (“universal probability”) as a starting point, and define complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately, a quantum state is simple if it is within a small distance from a low-dimens...
متن کاملOn Gács' quantum algorithmic entropy
We define an infinite dimensional modification of lower-semicomputability of density operators by Gács with an attempt to fix some problem in the paper. Our attempt is partly achieved by showing the existence of universal operator under some additional assumption. It is left as a future task to eliminate this assumption. We also see some properties and examples which stimulate further research....
متن کاملQuantum Dynamical Entropies and Gács Algorithmic Entropy
Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical) entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following,...
متن کاملAlgorithmic Entropy of Sets
In a previous paper a theory of program size formally identical to information theory was developed. The entropy of an individual finite object was defined to be the size in bits of the smallest program for calculating it. It was shown that this is − log2 of the probability that the object is obtained by means of a program whose successive bits are chosen by flipping an unbiased coin. Here a th...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2001
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/34/35/312