Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of everyday experience is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in open quantum systems. We show the generic appearance of objective results in quantum measurements, provided we macroscopically coarse-grain the measuring apparatus and wait long enough. To study genericity, we employ the widely used Gaussian unitary ensemble of random matrices and the Hoeffding inequality. We derive generic objectivization time scales, given solely by the interaction strength and the systems' dimensions. Our results are manifestly universal and are a generic property of von Neumann measurements.
A crucial question is how objective and classical behavior arises from a fundamental physical theory. Here we provide a natural definition of a decoherence process valid in all causal theories and show how its behavior can be extremely different from the quantum one. Remarkably, despite this, we prove that the so-called spectrum broadcast structure characterizes all objective states in every fundamental causal theory, exactly as in quantum mechanics. Our results show a stark contrast between the extraordinarily diverse decoherence behavior and the universal features of objectivity.
What happens when a quantum system undergoing unitary evolution in time is subject to repeated projective measurements to the initial state at random times? A question of general interest is: How does the survival probability
Sm, namely, the probability that an initial state survives even after
m number of measurements, behave as a function of
m? In the context of two paradigmatic quantum systems, one evolving in discrete and the other in continuous time, we present a wealth of numerical and analytical results that hint at the curious nature of quantum measurement dynamics. In particular, we unveil that when evolution after every projective measurement continues with the projected component of the instantaneous state, the average and the typical survival probability decay as an exponential in
m for large
m. By contrast, if the evolution continues with the leftover component, namely, what remains of the instantaneous state after a measurement has been performed, the survival probability decays asymptotically as a power law in
m with exponent
3/2. These results hold independently of the choice of the distribution of times between successive measurements, implying robustness and ubiquity of our derived results.
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first step in formalizing the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy, a notion that we call the measurement-equilibration hypothesis. In this paradigm, we investigate how classical measurement outcomes can emerge within a purely unitary framework, and find that (1) the interactions used in standard measurement models fail to spontaneously encode information classically and (2) while ideal projective measurements are impossible, one can (for a given form of Hamiltonian) approximate them exponentially well as more physical systems are collected together into an “observer” system. We thus lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.
Abstract Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.
We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-
1/2 systems only, and we hope will be useful in future objectivity experiments.