Relational physics with real rods and clocks and the measurement problem of quantum mechanics

The use of real clocks and measuring rods in quantum mechanics implies a natural loss of unitarity in the description of the theory. We briefly review this point and then discuss the implications it has for the measurement problem in quantum mechanics. The intrinsic loss of coherence allows to circumvent some of the usual objections to the measurement process as due to environmental decoherence.Comment: 19 pages, RevTex, no figure

Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint

In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$, but is independent of the choice of $\sigma$.Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment for Quantum Relative Entropy

Conditions for strictly purity-decreasing quantum Markovian dynamics

The purity, Tr(rho^2), measures how pure or mixed a quantum state rho is. It is well known that quantum dynamical semigroups that preserve the identity operator (which we refer to as unital) are strictly purity-decreasing transformations. Here we provide an almost complete characterization of the class of strictly purity-decreasing quantum dynamical semigroups. We show that in the case of finite-dimensional Hilbert spaces a dynamical semigroup is strictly purity-decreasing if and only if it is unital, while in the infinite dimensional case, unitality is only sufficient.Comment: 4 pages, no figures. Contribution to the special issue "Real-time dynamics in complex quantum systems" of Chemical Physics in honor of Phil Pechukas. v2: Simplified proof of theorem 1 and validity conditions clarifie

Quantum ratchets in dissipative chaotic systems

Using the method of quantum trajectories we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for implementation of the quantum ratchet effect with cold atoms in optical lattices.Comment: Significant changes: Several text improvements and new results. Figure 2 modified. Figure 4 adde

Models for local ohmic quantum dissipation

We construct model master equations for local quantum dissipation. The master equations are in the form of Lindblad generators, with imposed constraints that the dissipations be strictly linear (i.e. ohmic), isotropic and translationally invariant. A particular form for is chosen to satisfy the constraints. The resulting master equations are given in both the Schr\"odinger and Heisenberg forms. We obtain fluctuation-dissipation relations, and discuss the relaxation of average kinetic energy to effective thermal equilibrium values. We compare our results to the Dekker and the Caldeira-Leggett master equations. These master equations allow a more general approach to quantum dissipation and the dynamics of quantum coherence to account for the nontrivial system-environment coupling in a local environment.Comment: 19 pages, REVTEX, PSU/TH/12

Quantum decoherence in the theory of open systems

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.Comment: 6 pages; talk at the 3rd International Workshop "Quantum Physics and Communication" (QPC 2005), Dubna, Russia, 200

On the quantum, classical and total amount of correlations in a quantum state

We give an operational definition of the quantum, classical and total amount of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation one has to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation for the first time. As a byproduct, we obtain a direct, operational and elementary proof of strong subadditivity of quantum entropy.Comment: 12 pages ReVTeX4, 2 eps figures. v2 has some arguments clarified and references update

Structure of the Algebra of Effective Observables in Quantum Mechanics

A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is completely determined

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.Comment: Talk at the XI International Conference on Quantum Optics (ICQO'2006), May 2006, Minsk (Belarus), 9 page