Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus ''monitored'' by the environment. The resulting loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observable. This mechanism is very efficient even in the limit of weak coupling. Indeed, the classical limit of quantum theory---that is, both classically reversible equations of motion and classical states (trajectories in phase space rather than their superpositions) can be naturally attained when both the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological models can be justified in the framework of environment induced superselection. 24 refs., 3 figs.
Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus ''monitored'' by the environment. The resulting loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observable. This mechanism is very efficient even in the limit of weak coupling. Indeed, the classical limit of quantum theory---that is, both classically reversible equations of motion and classical states (trajectories in phase space rather than their superpositions) can be naturally attained when both the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological models can be justified in the framework of environment induced superselection. 24 refs., 3 figs.
Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus monitored'' by the environment. This causes the system to decohere.'' Loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observables. This mechanism is very efficient even in the limit of weak coupling to the environment. The classical limit of quantum theory -- that is, both classical irreversible equations of motion and classical states (trajectories in phase space rather than their superpositions) obtains in the limit in which the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological model can be justified in the framework of environment induced susperselection. 24 refs., 2 figs.
The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ``Schr\"odinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ``collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ``classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ``found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ``fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
We discuss the manner in which the gravitational field becomes classical in quantum cosmology. This involves two steps. First, one must show that the quantum state of the gravitational field becomes strongly peaked about a set of classical configurations. Second, one must show that the system is in one of a number of states of a relatively permanent nature that have negligible interference with each other. This second step involves decoherence---destruction of the off-diagonal terms in the density matrix, representing interference. To introduce the notion of decoherence, we discuss it in the context of the quantum theory of measurement, following the environment-induced superselection approach of Zurek. We then go on to discuss the application of these ideas to quantum cosmology. We show, in a simple homogeneous isotropic model, that the density matrix of the Universe will decohere if the long-wavelength modes of an inhomogeneous massless scalar field are traced out. These modes effectively act as an environment which continuously ``monitors'' the scale factor. The coherence width is very small except in the neighborhood of a classical bounce. This means that one cannot really say that a classical solution bounces because the notion of classical spacetime does not apply. The coherence width decreases as the scale factor increases, which has implications for the arrow of time. We also show, using decoherence arguments, that the WKB component of the wave function of the Universe which represents expanding universes has negligible interference with the collapsing component. This justifies the usual assumption that they may be treated separately.
The emergence of classical behavior in quantum theory is often ascribed to the interaction of a quantum system with its environment, which can be interpreted as environmental monitoring of the system. As a result, off-diagonal elements of the density matrix of the system are damped in the basis of a preferred observable, often taken to be the position, leading to the phenomenon of decoherence. This effect can be modeled dynamically in terms of a Lindblad equation driven by the position operator. Here the question of decoherence resulting from a monitoring of position and momentum, i.e., a phase-space measurement, by the environment is addressed. There is no standard quantum observable corresponding to the detection of phase-space points, which is forbidden by Heisenberg's uncertainty principle. This issue is addressed by use of a coherent-state-based positive operator-valued measure for modeling phase-space monitoring by the environment. In this scheme, decoherence in phase space implies the diagonalization of the density matrix in both position and momentum representations. This is shown to be linked to a Lindblad equation where position and momentum appear as two independent Lindblad operators.
In connection with the recent experiments on quantum measurement, such as the “which-way”detection using the Bragg scattering of cold atoms and quantum interference using a small molecular C 60 quantum system, we introduce the quantum measurement problem and its relevant fundamental concepts and ideas, such as quantum coherence, quantum decoherence and quantum entanglement. In order to understand the loss of quantum coherence for a quantum system due to its interaction with another system behaving classically or macroscopically, we discuss some quantum dynamical models to describe the quantum decoherence and quantum dissipation induced by couplings to the external environment or inner motions. In the classical or macroscopic limit, it is shown that the wave function of the total system formed by the quantum system plus another system interacting with it is factorized as an entangled state with correlation between the measured quantum states and the configurations of the external large system or the inner degrees of freedom. In association with a novel viewpoint about quantum measurement, which has been directly verified by recent experiments (e.g.,S. Durr et al., Nature,1998,33:359), it is shown that quantum entanglement is indeed responsible for the quantum decoherence, and thus it can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. These arguments give us a possible solution to the “Schrdinger cat paradox” and to whether the coherent superposition of macroscopic states exists. These discussions are also applied to the quantum decoherence problems in quantum information including quantum computing and quantum communication.
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.