Related papers: From free-evolution to tomographic representation
We construct and explore a family of states for quantum systems in contact with two or more heath reservoirs. The reservoirs are described by equilibrium distributions. The interaction of each reservoir with the bulk of the system is…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system…
We study solutions to the quantum trajectory evolution of $N$-mode open quantum systems possessing a time-independent Hamiltonian, linear Heisenberg-picture dynamics, and Gaussian measurement noise. In terms of the mode annihilation and…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the…
Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are…
A single photon has many physical degrees of freedom (DOF) that can carry the state of a high-dimensional quantum system. Nevertheless, only a single DOF is usually used in any specific demonstration. Furthermore, when more DOF are being…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in the generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
In the framework of the Heisenberg picture, an alternative derivation of the reduced density matrix of a driven dissipative quantum harmonic oscillator as the prototype of an open quantum system is investigated. The reduced density matrix…
We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a know time evolution for a desired period of time. Afterwards we perform a measurement with a…