Weak measurement and rapid state reduction in bipartite quantum systems

In this paper we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show 1) that the algorithm that maximizes the average purification rate is not the same as that that for a single qubit, and 2) that it is always possible to construct an algorithm that generates a deterministic rate of purification for {\em both} qubits. We also reveal a key difference between projective and continuous measurements with regard to state-purification.Comment: 4 pages, 3 figure

Bellman equations for optimal feedback control of qubit states

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.Comment: 10 pages, no figures, replaced the simpler model in section

Optimal Pointers for Joint Measurement of sigma-x and sigma-z via Homodyne Detection

We study a model of a two-level system (i.e. a qubit) in interaction with the electromagnetic field. By means of homodyne detection, one field-quadrature is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred into the field, thus influencing the homodyne measurement results. We construct random variables (pointers) on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of sigma-x and sigma-z. Using variational calculus, we find the pointers that are optimal. These optimal pointers are very close to hitting the bound imposed by Heisenberg's uncertainty relation on joint measurement of two non-commuting observables. We close the paper by giving the probability densities of the pointers.Comment: 20 pages, 13 figures, typos corrected, reference adde

Adaptive drift and barrier-avoidance by a fly-forage migrant along a climate-driven flyway

BACKGROUND: Route choice and travel performance of fly-forage migrants are partly driven by large-scale habitat availability, but it remains unclear to what extent wind support through large-scale wind regimes moulds their migratory behaviour. We aimed to determine to what extent a trans-equatorial fly-forage migrant engages in adaptive drift through distinct wind regimes and biomes across Africa. The Inter-tropical Front (ITF) marks a strong and seasonally shifting climatic boundary at the thermal equator, and we assessed whether migratory detours were associated with this climatic feature. Furthermore, we sought to disentangle the influence of wind and biome on daily, regional and seasonal travel performance. METHODS: We GPS-tracked 19 adult Eleonora’s falcons Falco eleonorae from the westernmost population on the Canary Islands across 39 autumn and 36 spring migrations to and from Madagascar. Tracks were annotated with wind data to assess the falcons’ orientation behaviour and the wind support they achieved in each season and distinct biomes. We further tested whether falcon routes across the Sahel were correlated with the ITF position, and how realized wind support and biome affect daily travel times, distances and speeds. RESULTS: Changes in orientation behaviour across Africa’s biomes were associated with changes in prevailing wind fields. Falcons realized higher wind support along their detours than was available along the shortest possible route by drifting through adverse autumn wind fields, but compromised wind support while detouring through supportive spring wind fields. Movements across the Sahel-Sudan zone were strongly associated to the ITF position in autumn, but were more individually variable in spring. Realized wind support was an important driver of daily travel speeds and distances, in conjunction with regional wind-independent variation in daily travel time budgets. CONCLUSIONS: Although daily travel time budgets of falcons vary independently from wind, their daily travel performance is strongly affected by orientation-dependent wind support. Falcons thereby tend to drift to minimize or avoid headwinds through opposing wind fields and over ecological barriers, while compensating through weak or supportive wind fields and over hospitable biomes. The ITF may offer a climatic leading line to fly-forage migrants in terms of both flight and foraging conditions. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s40462-021-00272-8

Correlated patterns in non-monotonic graded-response perceptrons

The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the overall performance of the perceptrons.Comment: 4 pages, 4 figure

Non Markovian Quantum Repeated Interactions and Measurements

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.Comment: 22 page

On the center of mass of Ising vectors

We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.Comment: 8 pages, 3 figures, LaTeX; Claims in connection with disordered systems have been withdrawn; More detailed description of the simulations; Inset added to figure