Related papers: Quantum stochastic differential equations and cont…
When a quantum system is monitored in continuous time, the result of the measurement is a stochastic process. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties…
The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
We develop the general quantum stochastic approach to the description of quantum measurements continuous in time. The framework, that we introduce, encompasses the various particular models for continuous-time measurements condsidered…
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants of time. This model of a "cloud chamber" allows to watch and…
We consider the theory of stopping bounded processes within the framework of Hudson--Parthasarathy quantum stochastic calculus, for both identity and vacuum adaptedness. This provides significant new insight into Coquio's method of stopping…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
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…
The theory of continuous quantum measurement allows to reconstruct the state $\rho_t$ of a system from a continuous stochastic measurement record $I_t$. However, this truly continuous-time signal $I_t$ is never available in practice. In…