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A practical measure for the complexity of sequences of symbols (" strings ") is introduced that is rooted in automata theory but avoids the problems of Kolmogorov–Chaitin complexity. This physical complexity can be estimated for ensembles of sequences, for which it reverts to the difference between the maximal entropy of the ensemble and the actual entropy(More)
We suggest that ensembles of self-replicating entities such as biological systems naturally evolve to a self-organized critical state in which fluctuations, as well as waiting times between phase transitions (" epochs "), are distributed according to a l/f " power law. Such distributions can explain observed frequency distributions in extinction events as(More)
We analyze properties of the quantum conditional amplitude operator ͓Phys. which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More(More)
We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann(More)
A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components ͑beam splitters, phase shifters, etc.͒. This suggests that the optical realization of(More)
We present a new tierra-inspired artiicial life system with local interactions and two-dimensional geometry , based on an update mechanism akin to that of 2D cellular automata. We nd that the spatial geometry is conducive to the development of diversity and thus improves adaptive capabilities. We also demonstrate the adaptive strength of the system by(More)