Related papers: Prediction and retrodiction with continuously moni…
We present a scheme to estimate Gaussian states of one-dimensional continuous variable systems, based on weak (unsharp) quantum measurements. The estimation of a Gaussian state requires us to find position ($q$), momentum ($p$) and their…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
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…
In a quantum system that is bounded by past and future conditions, weak continuous monitoring forward-evolving and backward-evolving quantum states are usually carried out separately. Therefore, measured signals at a given time t cannot be…
We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In…
Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random back action perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known…
We determine the quantum Cram\'er-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
We investigate the measurements of two-state quantum systems (qubits) at finite temperatures using a resonant harmonic oscillator as a quantum probe. The reduced density matrix and oscillator correlators are calculated by a scheme combining…
We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of…
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…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…
We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the…
Frequent observation of a quantum system leads to quantum Zeno physics, where the system evolution is constrained to states commensurate with the measurement outcome. We show that, more generally, the system can evolve between such states…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…