Related papers: Martingale Projections and Quantum Decoherence
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Transformations of transformations, also called higher-order transformations, is a natural concept in information processing, which has recently attracted significant interest in the study of quantum causal relations. In this work, a…
There is current interest in dynamical description of dif- ferent decompositions of a quantum system into subsystems. We investi- gate usefulness of the Nakajima-Zwanzig projection method in this context. Particularly, we are interested in…
Here we analyze the relationship between quantum contextuality and decoherence in interference experiments with matter particles by means of a simple reduced quantum-trajectory model, which attempts to simulate the behavior of the…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Standard semi-classical models of decoherence do not take explicit account of the classical information required to specify the system - environment boundary. I show that this information can be represented as a finite set of reference…
We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then…
Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global…
Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations}…
We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem…
The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued…
We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…
The standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances,…
The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit. This limit, and…
Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…