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

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

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

Environment Induced Entanglement in Markovian Dissipative Dynamics

We show that two, non interacting 2-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.Comment: 4 pages, LaTex, no figures, added reference

Quantum thermodynamics with missing reference frames: Decompositions of free energy into non-increasing components

If an absolute reference frame with respect to time, position, or orientation is missing one can only implement quantum operations which are covariant with respect to the corresponding unitary symmetry group G. Extending observations of Vaccaro et al., I argue that the free energy of a quantum system with G-invariant Hamiltonian then splits up into the Holevo information of the orbit of the state under the action of G and the free energy of its orbit average. These two kinds of free energy cannot be converted into each other. The first component is subadditive and the second superadditive; in the limit of infinitely many copies only the usual free energy matters. Refined splittings of free energy into more than two independent (non-increasing) terms can be defined by averaging over probability measures on G that differ from the Haar measure. Even in the presence of a reference frame, these results provide lower bounds on the amount of free energy that is lost after applying a covariant channel. If the channel properly decreases one of these quantities, it decreases the free energy necessarily at least by the same amount, since it is unable to convert the different forms of free energies into each other.Comment: 17 pages, latex, 1 figur

A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction

The optimal power performance of a first principle quantum heat engine model shows friction-like phenomena when the internal fluid Hamiltonian does not commute with the external control field. The model is based on interacting two-level-systems where the external magnetic field serves as a control variable.Comment: 4 pages 3 figure

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