Related papers: The Gambler's Ruin Problem and Quantum Measurement
A game in which one player makes unitary transformations of a simple system, and another seeks to confound the resulting state by a randomly chosen action is analyzed carefully. It is shown that the second player can reduce any system to a…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Quantum decoherence arises due to uncontrollable entanglement between a system with its environment. However the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to…
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
It is shown that having degenerate ground states over the domain of the wavefunction of a system is a sufficient condition for a quantum system to act as a measuring apparatus for the system. Measurements are then instances of spontaneous…
Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding…
Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous…
Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain…
We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence we assume Markovian approximation of open quantum…
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and…
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate $\tau^{-1}$ and the system-probe interaction strength $\gamma$ we derive…
We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it…
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…