We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about a particular system. The measurement apparatus is assumed to contain a large number of degrees of freedom, and the measurement outcomes are obtained by looking at the long interaction time limit. We study two cases which show contrasting behaviour. With a fixed axis coupling, the measurement is performed along the pointer basis with a high degree of robustness, for a wide variety of bath states. In a second model with Heisenberg interactions, the measurement outcomes can be altered considerably by changing the state of the bath.
We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about a particular system. The measurement apparatus is assumed to contain a large number of degrees of freedom, and the measurement outcomes are obtained by looking at the long interaction time limit. We study two cases which show contrasting behaviour. With a fixed axis coupling, the measurement is performed along the pointer basis with a high degree of robustness, for a wide variety of bath states. In a second model with Heisenberg interactions, the measurement outcomes can be altered considerably by changing the state of the bath.
We present an exact derivation of a process in which a microscopic measured system interacts with “heat bath ” and pointer modes of a measuring device, via a linear coupling involving Hermitian operator Λ of the system. In the limit of strong interaction with these modes, over a small time interval, we show that the measured system and the “pointer ” part of the measuring device evolve into a statistical mixture of direct-product states such that the system is in each eigenstate of Λ with the correct quantummechanical probability, whereas the expectation values of pointer-space operators retain amplified information of the system’s eigenstate. PACS: 03.65.Bz, 03.65.Ca – 1 – The problem of quantum measurement has fascinated scientists for a long time [1]. It has been argued that a large “bath ” is an essential ingredient of the measurement process. Interaction with the bath, which might be a “heat bath ” in thermal equilibrium, causes decoherence which is
A quantum measurement process, when non-trivial, is not a closed evolution: the appearance of classical outcomes is usually interpreted as the evidence of some decoherence-like mechanism causing quantum superpositions to degrade into classical mixtures. Such mechanism is due to a net flow of information from the input system (measurement object), through the physical apparatus interacting with the object (measurement probe), into some environment, the latter representing all those degrees of freedom which are not directly accessible by the experimenter. For this reason, the phenomenon of state reduction induced by the measurement process generally entails an irreversible state change. The aim of our contribution is to answer the following questions : how much information a measurement is able to extract? "How much" irreversible is the state reduction due to a particular measurement process? In which way information gain and irreversibility are related?
Traditionally, quantum measurements have been associated with irreversible transformations of pure states into mixtures. In this paper we show that this old hypothesis is redundant. A simple model is constructed in which the measuring process is described by a continuous unitary transformation of the state vector of the observed system and the apparatus. The final state is pure, but appears to be a mixture if we ignore the degrees of freedom of the apparatus. This property is most strikingly illustrated by reformulating the problem in the Heisenberg picture: The state vector is fixed, and the dynamical variables are changed by the measurement.
A transition would lead the system from its original superposition state to another state, in which the system and the measuring apparatus acquire definite properties. The problem of measurement is approached from the theory of environment-induced decoherence. This theoretical program, based on the study of the effects of the interaction between a quantum system, is considered as an open system and its environment. In turn, even the measurement problem has been reformulated, expanding its scope. As Schlosshauer points out, the conceptual difficulties of quantum measurement can now be concentrated around two cases: The definite outcome, which consists of the traditional question about quantum measurement. The problem of the preferred basis: since there is a theoretical ambiguity in the definition of the observable measured due to the mathematical possibility of a base change in the expression of the system state.
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the condensate, is the pointer variable. It is shown that properties of irreversibility and ergodicity breaking, which are inherent in the model apparatus, ensure the appearance of definite results of the measurement, and provide a dynamical realization of wave-function reduction or collapse. The measurement process takes place in two steps: First, the reduction of the state of the tested system occurs over a time of order $\ensuremath{\Elzxh}{/(TN}^{1/4}),$ where T is the temperature of the apparatus, and N is the number of its degrees of freedom. This decoherence process is governed by the apparatus-system interaction. During the second step classical correlations are established between the apparatus and the tested system over the much longer time scale of equilibration of the apparatus. The influence of the parameters of the model on nonideality of the measurement is discussed. Schr\"odinger kittens, EPR setups, and information transfer are analyzed.
In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for the interpretation of quantum mechanics. Here we analyse an ideal measurement as a process of interaction between the tested system S and an apparatus A, so as to derive the properties postulated in textbooks. We thus consider within standard quantum mechanics the measurement of a quantum spin component ŝz by an apparatus A, being a magnet coupled to a bath. We first consider the evolution of the density operator of S + A describing a large set of runs of the measurement process. The approach describes the disappearance of the off-diagonal terms ("truncation") of the density matrix as a physical effect due to A, while the registration of the outcome has classical features due to the large size of the pointer variable, the magnetization. A quantum ambiguity implies that the density matrix at the final time can be decomposed on many bases, not only the one of the measurement. This quantum oddity prevents to connect individual outcomes to measurements, a difficulty known as the "measurement problem". It is shown that it is circumvented by the apparatus as well, since the evolution in a small time interval erases all decompositions, except the one on the measurement basis. Once one can derive the outcome of individual events from quantum theory, the so-called collapse of the wavefunction or the reduction of the state appears as the result of a selection of runs among the original large set. Hence nothing more than standard quantum mechanics is needed to explain features of measurements. The employed statistical formulation is advocated for the teaching of quantum theory.