Ground-state Stabilization of Open Quantum Systems by Dissipation

Control by dissipation, or environment engineering, constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems. The system-environment coupling, often considered to be detrimental to quantum coherence, also provides the means to steer the system to desired states. This paper aims to develop the theory for engineering of the dissipation, based on a ground-state Lyapunov stability analysis of open quantum systems via a Heisenberg-picture approach. Algebraic conditions concerning the ground-state stability and scalability of quantum systems are obtained. In particular, Lyapunov stability conditions expressed as operator inequalities allow a purely algebraic treatment of the environment engineering problem, which facilitates the integration of quantum components into a large-scale quantum system and draws an explicit connection to the classical theory of vector Lyapunov functions and decomposition-aggregation methods for control of complex systems. The implications of the results in relation to dissipative quantum computing and state engineering are also discussed in this paper.Comment: 18 pages, to appear in Automatic

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.Comment: 31 page

Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem

Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure could be taken as the error of adiabatic approximation. We prove under certain conditions, this error can be precisely estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example on which the applicability of the adiabatic theorem is questionable.Comment: 12 pages, to appear in EPJ Quantum Technolog

A posteriori teleportation ?

Braunstein and Kimble observe correctly that, in the Innsbruck experiment, Nature 390, 575 (1997), one does not always observe a teleported photon conditioned on a coincidence recording at the Bell-state analyser. However, when a teleported photon appears, it has all the properties required by the teleportation protocol.Comment: 1 page LaTeX. Reply to a comment by S.L. Braunstein and H.J. Kimble, Nature 394, 840-841 (1998) and quant-ph/981000

Quantum Unique Ergodicity for Eisenstein Series in the Level Aspect

We prove a variety of quantum unique ergodicity results for Eisenstein series in the level aspect. A new feature of this variant of QUE is that the main term involves the logarithmic derivative of a Dirichlet $L$-function on the $1$-line. A zero of this $L$-function near the $1$-line can thus have a distorting effect on the main term. We obtain quantitative control on the test function and thereby prove an asymptotic formula in the level aspect version of the problem with test functions of shrinking support. Surprisingly, this asymptotic formula shows some obstruction to equidistribution that may retrospectively be interpreted as being caused by the growth of Eisenstein series in the cusps. We also make some coarse descriptions on the unevenness of the mass distribution of level $N$ Eisenstein series on the fibers of the canonical projection map from $Y_0(N)$ to $Y_0(1)$.Comment: Multiple updates thanks to the referee

A Flexible Method for Conducting Power Analysis for Two- and Three-Level Hierarchical Linear Models in R

A general approach for conducting power analysis in two- and three-level hierarchical linear models (HLMs) is described. The method can be used to perform power analysis to detect fixed effects at any level of a HLM with dichotomous or continuous covariates. It can easily be extended to perform power analysis for functions of parameters. Important steps in the derivation of this approach are illustrated and numerical examples are provided. Sample code implementing this approach is provided using the free program R

Evidence for Respiratory Neuromodulator Interdependence after Cholinergic Disruption in the Ventral Respiratory Column

Reverse dialysis of the muscarinic receptor antagonist, atropine (ATR, 50 mM), into the pre-Bötzinger Complex region of the ventral respiratory column (VRC) of awake and sleeping goats increases breathing frequency and serotonin (5-HT), substance P (SP), glycine, and GABA concentrations in the effluent dialysate. Herein, we report data from goats in which we reverse dialyzed 5 mM ATR or specific antagonists of M2 or M3 muscarinic receptors into the VRC. The effects on frequency of all three antagonists were not significantly different from time control studies. 5 mM ATR and the M3 antagonist increased SP sevenfold less than 50 mM ATR. The antagonists had no effect on 5-HT, glycine, and/or GABA, suggesting that the increases in glycine and GABA with 50 mM ATR were secondary to the larger increases in 5-HT and/or SP. These data are suggestive of neuromodulator interdependence, whereby attenuation of one neuromodulator is compensated for by local changes in other neuromodulators to stabilize breathing