Introduction to Decoherence Theory

Abstract

This introduction to the theory of decoherence is aimed at readers with an interest in the science of quantum information. In that field, one is usually content with simple, abstract descriptions of non-unitary "quantum channels" to account for imperfections in quantum processing tasks. However, in order to justify such models of non-unitary evolution and to understand their limits of applicability it is important to know their physical basis. I will therefore emphasize the dynamic and microscopic origins of the phenomenon of decoherence, and will relate it to concepts from quantum information where applicable, in particular to the theory of quantum measurement.The study of decoherence, though based at the heart of quantum theory, is a relatively young subject. It was initiated in the 1970's and 1980's with the work of H. D. Zeh and W. Zurek on the emergence of classicality in the quantum framework. Until that time the orthodox interpretation of quantum mechanics dominated, with its strict distinction between the classical macroscopic world and the microscopic quantum realm. The mainstream attitude concerning the boundary between the quantum and the classical was that this was a purely philosophical problem, intangible by any physical analysis. This changed with the understanding that there is no need for denying quantum mechanics to hold even macroscopically, if one is only able to understand within the framework of quantum mechanics why the macro-world appears to be classical. For instance, macroscopic objects are found in approximate position eigenstates of their center-of-mass, but never in superpositions of macroscopically distinct positions. The original motivation for the study of decoherence was to explain these effective super-selection rules and the apparent emergence of classicality within quantum theory by appreciating the crucial role played by the environment of a quantum system. Hence, the relevant theoretical framework for the study of decoherence is the theory of open quantum systems, which treats the effects of an unThis text corresponds to a chapter in: A. Buchleitner, C. Viviescas, and M. Tiersch (Eds.), Entanglement and Decoherence.

Unification of different views of decoherence and discord

“…The first definition is well-known [1][2][3][4] and, e.g., has been linked to the loss of interference in a two-slit interferometer (TSI) (e.g. [3]).…”

“…[3]). The second definition [1][2][3][4][5][6][7][8], also linked to loss of interference in a TSI [9,10], has been connected to objectivity when many copies of information go off to the environment [5], though the present article is only concerned with whether or not a single copy exists in the environment. In (D3), our notion of complementary information will become more precise later, we simply note that the complementary information is the kind of information that is directly responsible for interference (which-phase information).…”

Quantum coherence and entanglement preservation in Markovian and non-Markovian dynamics via additional qubits

“…(12), the correlation function f (t) can be calculated by using Eq. (11), therefore we have 4) and its Laplace transform is written as…”

“…However, the quantum entanglement is so fragile and undergoes either an asymptotic decay or a sudden death [4,5]. This is due to decoherence, whereby the unavoidable interaction between any real quantum system with its surrounding environment alters the quantum system and consequently disentanglement occurs.…”

A density tensor hierarchy for open system dynamics: retrieving the noise

“…For further details, and in particular a discussion of the physical justification for the approximations involved, see Sec. 3.3 of ref [1] and also ref [13]. One assumes that H ℓ (t) has the form …”