Related papers: Symmetries and ergodic properties in quantum proba…
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition operators for non-commutative stochastic processes can be…
Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations, which can be used to…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
Motivated by reformulating Furstenberg's $\times p,\times q$ conjecture via representations of a crossed product $C^*$-algebra, we show that in a discrete $C^*$-dynamical system $(A,\Gamma)$, the space of (ergodic) $\Gamma$-invariant states…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for…
We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states…