System information propagation for composite structures

Abstract

We study in details decoherence process of a spin register, coupled to a spin environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available to multiple observations. This process is more subtle than in a case of a single qubit due to possible presence of protected subspaces: Decoherence free subspaces and, so called, orthogonalization free subspaces. We show that this leads to a rich structure of coherence loss/protection in the asymptotic state of the register and a part of its environment. We formulate a series of examples illustrating these structures.

Entanglement and objectivity in pure dephasing models

“…The measurement Hamiltonian which is used to study the emergence of spectrum broadcast structure states is, in fact a special case of the general Hamiltonian which leads to pure dephasing evolutions [6][7][8][9][10][11][12][13] in a systemenvironment scenario [30,31]. The Hamiltonian is given byĤ…”

“…For the density matrix of the system and observed environments to be an SBS state, a second requirement is necessary, namely that the observed environment density matrices conditional on the system pointer states,ρ k ii (t), be perfectly distinguishable. This in turn is equivalent to them being orthogonal, in the sense of having orthogonal supportsρ k ii (t)ρ k jj (t) = 0 (12) for every pair of system pointer states, i = j, and for all observed environments k. Only then can the system states be uniquely determined by measurements on any of the environments, without damaging either the system state or the states of the environments themselves [4,5].…”

“…[32]). But QEE alone is not sufficient for the emergence of objectivity even for qubit systems, since the condition for QEE generation,ρ k ii (t) =ρ k jj (t), is much weaker than the condition (12). We study the latter in more detail in the next Section.…”

“…In realistic situations one can hardly expect such strict fulfillment (see e.g. [6][7][8][9][10][11][12][13]) and some measure of distinguishability [33,34], like the state fidelity, must be used. Nevertheless it is interesting to study the ideal situation and use it to infer about the behavior of systems which do not show strict orthogonality, but do exhibit the generation of systemenvironment entanglement.…”

“…To study situations when the emergence of objectivity is possible in the above sense of SBS creation, typically system-environment interactions are taken into account which lead to pure dephasing of the qubit [6][7][8][9][10][11][12][13] after the environmental degrees of freedom are traced out. These types of interactions describe situations when the T * 2 times are much shorter than the T 1 times (the decay of phase coherence is much faster than relaxation) are fairly common in solid state scenarios.…”