Abstract:
Measurements --- interactions which establish correlations between a system and a recording device --- can be made thermodynamically reversible. One might be concerned that such reversibility will make the second law of thermodynamics vulnerable to the designs of the demon of choice, a selective version of Maxwell's demon. The strategy of the demon of choice is to take advantage of rare fluctuations to extract useful work, and to reversibly undo measurements which do not lead to such a favorable but unlikely outcomes. I show that this threat does not arise as the demon of choice cannot operate without recording (explicitely or implicitely) whether its measurement was a success (or a failure). Thermodynamic cost associated with such a record cannot be, on the average, made smaller than the gain of useful work derived from the fluctuations.

Abstract:
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a classical system can exist independently from its state. In quantum theory this is no longer possible: In an isolated quantum system the state and the information about it are inextricably linked, and any measurement may -- and usually will -- reset that state. However, when the information about the state of a quantum system is spread throughout the environment, it can be treated (almost) as in classical physics.

Abstract:
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like'' states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Born's rule, $p_k \propto |\psi_k|^2$ for the outcomes associated with Schmidt states. Probabilities derived in this manner are an objective reflection of the underlying state of the system -- they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge'' of the observer. Envariance - based approach is compared with and found superior to pre-quantum definitions of probability including the {\it standard definition} based on the `principle of indifference' due to Laplace, and the {\it relative frequency approach} advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Born's rule: Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence. Envariant origin of Born's rule for probabilities sheds a new light on the relation between ignorance (and hence, information) and the nature of quantum states.

Abstract:
I introduce environment - assisted invariance -- a symmetry related to causality that is exhibited by correlated quantum states -- and describe how it can be used to understand the nature of ignorance and, hence, the origin of probabilities in quantum physics.

Abstract:
We introduce and investigate a simple model of conditional quantum dynamics. It allows for a discussion of the information-theoretic aspects of quantum measurements, decoherence, and environment-induced superselection (einselection).

Abstract:
We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a "slow" detector. Such a detector is only sensitive to slowly-changing variables, e. g. energy, while its back-action can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.

Abstract:
Adiabaticity of quantum evolution is important in many settings. One example is the adiabatic quantum computation. Nevertheless, up to now, there is no effective method to test the adiabaticity of the evolution when the eigenenergies of the driven Hamiltonian are not known. We propose a simple method to check adiabaticity of a quantum process for an arbitrary quantum system. We further propose a operational method for finding a uniformly adiabatic quench scheme based on Kibble-Zurek mechanism for the case when the initial and the final Hamiltonians are given. This method should help in implementing adiabatic quantum computation.

Abstract:
We study phase transition from the Mott insulator to superfluid in a periodic optical lattice. Kibble-Zurek mechanism predicts buildup of winding number through random walk of BEC phases, with the step size scaling as a the third root of transition rate. We confirm this and demonstrate that this scaling accounts for the net winding number after the transition.

Abstract:
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum analogs of systems which exhibit classical hamiltonian chaos entropy production rate quickly tends to a constant which is given by the sum of the positive Lyapunov exponents, and falls off only as the system approaches equilibrium. By contrast, integrable systems tend to have entropy production rate which decreases as $t^{-1}$ well before equilibrium is attained. Thus, behavior of quantum systems in contact with the environment can be used as a test to determine the nature of their hamiltonian evolution.

Abstract:
A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. We use quantum kinetic theory to show that this mechanism, originally postulated in the cosmological context, and analysed so far only on the mean field classical level, should allow spontaneous generation of vortex lines in trapped Bose-Einstein condensates of simple topology, or of winding number in toroidal condensates.