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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)
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems,(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)
We describe and investigate the learning capabilities displayed by a population of self-replicating segments of computer code subject to random mutation: the tierra environment. We find that learning is achieved through phase transitions that adapt the population to the environment it encounters, at a rate characterized by external parameters such as(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 theoretical as well as experimental investigation of a population of self-replicating segments of code subject to random mutation and survival of the ttest. Under the assumption that such a system constitutes a minimal system with characteristics of life, we obtain a number of statements on the evolution of complexity and the trade-oo between(More)