Quantum control theory and applications: A survey

This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective, some references are added, published versio

Noise-robust quantum sensing via optimal multi-probe spectroscopy

The dynamics of quantum systems are unavoidably influenced by their environment and in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.Comment: 13 pages, 14 figure

Distant Entanglement of Macroscopic Gas Samples

One of the main ingredients in most quantum information protocols is a reliable source of two entangled systems. Such systems have been generated experimentally several years ago for light but has only in the past few years been demonstrated for atomic systems. None of these approaches however involve two atomic systems situated in separate environments. This is necessary for the creation of entanglement over arbitrary distances which is required for many quantum information protocols such as atomic teleportation. We present an experimental realization of such distant entanglement based on an adaptation of the entanglement of macroscopic gas samples containing about 10^11 cesium atoms shown previously by our group. The entanglement is generated via the off-resonant Kerr interaction between the atomic samples and a pulse of light. The achieved entanglement distance is 0.35m but can be scaled arbitrarily. The feasibility of an implementation of various quantum information protocols using macroscopic samples of atoms has therefore been greatly increased. We also present a theoretical modeling in terms of canonical position and momentum operators X and P describing the entanglement generation and verification in presence of decoherence mechanisms.Comment: 20 pages book-style, 3 figure

Optimized experimental settings for the best detection of quantum nonlocality

Nonlocality lies at the core of quantum mechanics from both a fundamental and applicative point of view. It is typically revealed by a Bell test, that is by violation of a Bell inequality, whose success depends both on the state of the system and on parameters linked to experimental settings. This leads to find, given the state, optimized parameters for a successful test. Here we provide, for a quite general class of quantum states, the explicit expressions of these optimized parameters and point out that, for a continuous change of the state, the corresponding suitable experimental settings may unexpectedly vary discontinuously. We finally show in a paradigmatic open quantum system that this abrupt "jump" of the experimental settings may even occur during the time evolution of the system. These jumps must be taken into account in order not to compromise the correct detection of nonlocality in the system.Comment: 5 pages, 2 figure

Signatures of the collapse and revival of a spin Schr\"{o}dinger cat state in a continuously monitored field mode

We study the effects of continuous measurement of the field mode during the collapse and revival of spin Schr\"{o}dinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the collapse and revival of a spin Schr\"{o}dinger cat state.Comment: 5 pages, 2 figure