Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics

Open system effects on slow light and electromagnetically induced transparency

The coherence properties of a three-level $\Lambda$-system influenced by a Markovian environment are analyzed. A coherence vector formalism is used and a vector form of the Lindblad equation is derived. Together with decay channels from the upper state, open system channels acting on the subspace of the two lower states are investigated, i.e., depolarization, dephasing, and amplitude damping channels. We derive an analytic expression for the coherence vector and the concomitant optical susceptibility, and analyze how the different channels influence the optical response. This response depends non-trivially on the type of open system interaction present, and even gain can be obtained. We also present a geometrical visualization of the coherence vector as an aid to understand the system response.Comment: Several changes; journal reference adde

Quantum Conditions on Dynamics and Control in Open Systems

Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace $H_{0}$ of dimensionality $M_{0}$, which evolves to populate system subspaces $H_{1}$, $H_{2}$ of dimensionality $M_{1}$, $M_{2}$. Then there always exists an initial state in $H_0$ that does not evolve into $H_2$ if $M_{0}>dM_{2},$ where $2 \leq d \leq (M_0 +M_1 +M_2)^2$ is the number of operators in the Kraus representation. Note, significantly, that the maximum $d$ can be far smaller than the dimension of the bath. If this condition is not satisfied then dynamics from $H_{0}$ that avoids $H_{2}$ can only be attained physically under stringent conditions. An example from molecular dynamics and spectroscopy, i.e. donor to acceptor energy transfer, is provided.Comment: 4 pages, no figur

Negativity and quantum discord in Davies environments

We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies--type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dephasing), both, the quantum discord and negativity decay to zero in the long time limit. In presence of a manifest dissipative dynamics, the entanglement negativity undergoes a sudden death at finite time while the quantum discord relaxes continuously to zero with increasing time. We find that in dephasing environments the decay of the negativity is more propitious with increasing time; in contrast, the evolving decay of the quantum discord proceeds weaker for dissipative environments. Particularly, the slowest decay of the quantum discord emerges when the energy relaxation time matches the dephasing time.Comment: submitted for publicatio

Dissipation and decoherence in photon interferometry

The propagation of polarized photons in optical media can be effectively modeled by means of quantum dynamical semigroups. These generalized time evolutions consistently describe phenomena leading to loss of phase coherence and dissipation originating from the interaction with a large, external environment. High sensitive experiments in the laboratory can provide stringent bounds on the fundamental energy scale that characterizes these non-standard effects.Comment: 14 pages, plain-Te

Bures and Statistical Distance for Squeezed Thermal States

We compute the Bures distance between two thermal squeezed states and deduce the Statistical Distance metric. By computing the curvature of this metric we can identify regions of parameter space most sensitive to changes in these parameters and thus lead to optimum detection statistics.Comment: 15 pages, 1 figure (not included - obtain from Author) To appear in Journal of Physics

Planck's scale dissipative effects in atom interferometry

Atom interferometers can be used to study phenomena leading to irreversibility and dissipation, induced by the dynamics of fundamental objects (strings and branes) at a large mass scale. Using an effective, but physically consistent description in terms of a master equation of Lindblad form, the modifications of the interferometric pattern induced by the new phenomena are analyzed in detail. We find that present experimental devices can in principle provide stringent bounds on the new effects.Comment: 12 pages, plain-Te

Effective dissipative dynamics for polarized photons

In the framework of open quantum systems, the propagation of polarized photons can be effectively described using quantum dynamical semigroups. These extended time-evolutions induce irreversibility and dissipation. Planned, high sensitive experiments, both in the laboratory and in space, will be able to put stringent bounds on these non-standard effects.Comment: 15 pages, plain-TeX, no figure

Open Quantum Dynamics: Complete Positivity and Entanglement

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behaviour of bipartite systems immersed in a same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.Comment: LaTex, 77 page

Fractional Generalization of Quantum Markovian Master Equation

We prove a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators are infinitesimal generators of completely positive semigroups and describe the properties of this semigroup. We solve the proposed fractional quantum Markovian equation for the harmonic oscillator with linear friction. A fractional power of the Markovian superoperator can be considered a parameter describing a measure of "screening" of the environment of the quantum system: the environmental influence on the system is absent for $\alpha=0$, the environment completely influences the system for $\alpha=1$, and we have a powerlike environmental influence for $0<\alpha<1$.Comment: 25 pages, LaTe