Quantum decoherence is the loss of quantum coherence. It involves generally a loss of information of a system to its environment. Quantum decoherence has been studied to understand how quantum systems convert to systems that can be explained by classical mechanics. Beginning out of attempts to extend the understanding of quantum mechanics, the theory has developed in several directions and experimental studies have confirmed some of the key issues. Quantum computing relies on quantum coherence and is one of the primary practical applications of the concept.
Concept In quantum mechanics, a physical system is described by a mathematical representation called a quantum state. Probabilities for the outcomes of experiments upon a system are calculated by applying the Born rule to the quantum state describing that system. Quantum states are either pure or mixed; pure states are also known as wavefunctions. Assigning a pure state to a quantum system implies certainty about the outcome of some measurement on that system, i.e., that there exists a measurement for which one of the possible outcomes will occur with probability 1. In the absence of outside forces or interactions, a quantum state evolves unitarily over time. Consequently, a pure quantum state remains pure. However, if the system is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time — a process called quantum decoherence or environmental decoherence. The quantum coherence is not lost but rather mixed with many more degrees of freedom in the environment, analogous to the way energy appears to be lost during friction in classical mechanics when it actually has produced heat in the environment.
Decoherence can be viewed as the loss of information from a system into the environment (often modelled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion). Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings.
History and interpretation Relation to interpretation of quantum mechanics An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum physics might correspond to experienced reality. Decoherence calculations can be done in any interpretation of quantum mechanics, since those calculations are an application of the standard mathematical tools of quantum theory. However, the subject of decoherence has been closely related to the problem of interpretation throughout its history.
Decoherence has been used to understand the possibility of the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse. It only provides a framework for apparent wave-function collapse, as the components of a quantum system entangle with other quantum systems within the same environment. That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.
With respect to the measurement problem, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, observation indicates that this mixture looks like a proper quantum ensemble in a measurement situation, as the measurements lead to the "realization" of precisely one state in the "ensemble".
The philosophical views of Werner Heisenberg and Niels Bohr have often been grouped together as the "Copenhagen interpretation", despite significant divergences between them on important points. In 1955, Heisenberg suggested that the interaction of a system with its surrounding environment would eliminate quantum interference effects. However, Heisenberg did not provide a detailed account of how this might transpire, nor did he make explicit the importance of entanglement in the process.
Origin of the concepts Nevill Mott's solution to the iconic Mott problem in 1929 is considered in retrospect to be the first quantum decoherence work. It was cited by the first modern theoretical treatment.
Although he did not use the term, the concept of quantum decoherence was first introduced in 1951 by the American physicist David Bohm, who called it the "destruction of interference in the process of measurement". Bohm later used decoherence to handle the measurement process in the de Broglie-Bohm interpretation of quantum theory.
The significance of decoherence was further highlighted in 1970 by the German physicist H. Dieter Zeh, and it has been a subject of active research since the 1980s. Decoherence has been developed into a complete framework, but there is controversy as to whether it solves the measurement problem, as the founders of decoherence theory admit in their seminal papers.
The study of decoherence as a proper subject began in 1970, with H. Dieter Zeh's paper "On the Interpretation of Measurement in Quantum Theory". Zeh regarded the wavefunction as a physical entity, rather than a calculational device or a compendium of statistical information (as is typical for Copenhagen-type interpretations), and he proposed that it should evolve unitarily, in accord with the Schrödinger equation, at all times. Zeh was initially unaware of Hugh Everett III's earlier work, which also proposed a universal wavefunction evolving unitarily; he revised his paper to reference Everett after learning of Everett's "relative-state interpretation" through an article by Bryce DeWitt. (DeWitt was the one who termed Everett's proposal the many-worlds interpretation, by which name it is commonly known.) For Zeh, the question of how to interpret quantum mechanics was of key importance, and an interpretation along the lines of Everett's was the most natural. Partly because of a general disinterest among physicists for interpretational questions, Zeh's work remained comparatively neglected until the early 1980s, when two papers by Wojciech Zurek invigorated the subject. Unlike Zeh's publications, Zurek's articles were fairly agnostic about interpretation, focusing instead on specific problems of density-matrix dynamics. Zurek's interest in decoherence stemmed from furthering Bohr's analysis of the double-slit experiment in his reply to the Einstein–Podolsky–Rosen paradox, work he had undertaken with Bill Wootters, and he has since argued that decoherence brings a kind of rapprochement between Everettian and Copenhagen-type views.
Decoherence does not claim to provide a mechanism for some actual wave-function collapse; rather it puts forth a reasonable framework for the appearance of wave-function collapse. The quantum nature of the system is simply entangled into the environment so that a total superposition of the wave function still exists, but exists—at least for all practical purposes—beyond the realm of measurement.Roger Penrose (2004), The Road to Reality, pp. 802–803: "...the environmental-decoherence viewpoint [...] maintains that state vector reduction [the R process] can be understood as coming about because the environmental system under consideration becomes inextricably entangled with its environment. [...] We think of the environment as extremely complicated and essentially 'random' [...], accordingly we sum over the unknown states in the environment to obtain a density matrix [...] Under normal circumstances, one must regard the density matrix as some kind of approximation to the whole quantum truth. For there is no general principle providing an absolute bar to extracting information from the environment. [...] Accordingly, such descriptions are referred to as FAPP [for all practical purposes]".Huw Price (1996), Times' Arrow and Archimedes' Point, p. 226: "There is a world of difference between saying 'the environment explains why collapse happens where it does' and saying 'the environment explains why collapse seems to happen even though it doesn't really happen'." By definition, the claim that a merged but unmeasurable wave function still exists cannot be proven experimentally. Decoherence is needed to understand why a quantum system begins to obey classical probability rules after interacting with its environment (due to the suppression of the interference terms when applying Born's probability rules to the system).
Criticism of the adequacy of decoherence theory to solve the measurement problem has been expressed by Anthony Leggett.
Mechanisms To examine how decoherence operates, an "intuitive" model is presented below. The model requires some familiarity with quantum theory basics. Analogies are made between visualizable classical phase spaces and Hilbert spaces. A more rigorous derivation in Dirac notation shows how decoherence destroys interference effects and the "quantum nature" of systems. Next, the density matrix approach is presented for perspective.
Phase-space picture An N-particle system can be represented in non-relativistic quantum mechanics by a wave function , where each xi is a point in 3-dimensional space. This has analogies with the classical phase space. A classical phase space contains a real-valued function in 6N dimensions (each particle contributes 3 spatial coordinates and 3 momenta). In this case a "quantum" phase space, on the other hand, involves a complex-valued function on a 3N-dimensional space. The position and momenta are represented by operators that do not commute, and lives in the mathematical structure of a Hilbert space. Aside from these differences, however, the rough analogy holds.
Different previously isolated, non-interacting systems occupy different phase spaces. Alternatively we can say that they occupy different lower-dimensional subspaces in the phase space of the joint system. The effective dimensionality of a system's phase space is the number of degrees of freedom present, which—in non-relativistic models—is 6 times the number of a system's free particles. For a macroscopic system this will be a very large dimensionality. When two systems (the environment being one system) start to interact, though, their associated state vectors are no longer constrained to the subspaces. Instead the combined state vector time-evolves a path through the "larger volume", whose dimensionality is the product of the dimensions of the two subspaces. The extent to which two vectors interfere with each other is a measure of how "close" they are to each other (formally, their overlap or Hilbert space multiplies together) in the phase space. When a system couples to an external environment, the dimensionality of, and hence "volume" available to, the joint state vector increases enormously. Each environmental degree of freedom contributes an extra dimension.