N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Journal of Statistical Mechanics: theory and experiment

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? Here, we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.

/pdf/quantum-correlations-with-no-causal-order-4bnxcvkqvj.pdf

Quantum correlations with no causal order

A machine equivalent to Turing machine, that is more intuitive in its working is defined. Three derivation rules are added to Elementary Arithmetic of Godel and his incompleteness theorems are proved without using any metalanguage. Two axioms are added to Zermelo-Fraenkel theory to derive the Continuum Hypothesis and to split the unit interval into infinitesimals.

Foundations of Computer Science

http://inspirehep.net/record/1207071/files/arXiv:1212.2839.pdf

Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

The present paper is both a review on the Feynman problem, and an original research presentation on the relations between Fermionic theories and qubits theories, both regarded in the novel framework of operational probabilistic theories. The most relevant results about the Feynman problem of simulating Fermions with qubits are reviewed, and in the light of the new original results, the problem is solved. The answer is twofold. On the computational side, the two theories are equivalent, as shown by Bravyi and Kitaev [S. B. Bravyi and A. Y. Kitaev, Ann. Phys. 298, 210 (2002)]. On the operational side, the quantum theory of qubits and the quantum theory of Fermions are different, mostly in the notion of locality, with striking consequences on entanglement. Thus the emulation does not respect locality, as it was suspected by Feynman [R. Feynman, Int. J. Theor. Phys. 21, 467 (1982)].

The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory

We show that the computational model based on local fermionic modes in place of qubits does not satisfy local tomography and monogamy of entanglement, and has mixed states with maximal entanglement of formation. These features directly follow from the parity superselection rule. We generalize quantum superselection rules to general probabilistic theories as sets of linear constraints on the convex set of states. We then provide a link between the cardinality of the superselection rule and the degree of holism of the resulting theory.

https://iopscience.iop.org/article/10.1209/0295-5075/107/20009/pdf

Fermionic computation is non-local tomographic and violates monogamy of entanglement

It is shown how a doubly special relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the -space, with an additional invariant given by the wave vector . The space-time reconstructed from the -space is intrinsically quantum, and exhibits the phenomenon of relative locality.

Doubly-Special Relativity from Quantum Cellular Automata

We study the dynamical behavior of a quantum cellular automaton which reproduces the Dirac dynamics in the limit of small wave vectors and masses. We present analytical evaluations along with computer simulations, showing that the automaton exhibits typical Dirac dynamical features, such as the Zitterbewegung and, considering the scattering from potential, the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical, and atomic-physics quantum simulators.

Alessandro Tosini

Papers

Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory

Fermionic computation is non-local tomographic and violates monogamy of entanglement

Doubly-Special Relativity from Quantum Cellular Automata

Dirac quantum cellular automaton in one dimension: Zitterbewegung and scattering from potential