Sensitivity optimization in quantum parameter estimation

We present a general framework for sensitivity optimization in quantum parameter estimation schemes based on continuous (indirect) observation of a dynamical system. As an illustrative example, we analyze the canonical scenario of monitoring the position of a free mass or harmonic oscillator to detect weak classical forces. We show that our framework allows the consideration of sensitivity scheduling as well as estimation strategies for non-stationary signals, leading us to propose corresponding generalizations of the Standard Quantum Limit for force detection.Comment: 15 pages, RevTe

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

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

Information Effect of Entry Into Credit Ratings Market: The Case of Insurers\u27 Ratings

The paper analyzes the effect of competition between credit rating agencies (CRAs) on the information content of ratings. We show that a monopolistic CRA pools sellers into multiple rating classes and has partial market coverage. This provides an opportunity for market entry. The entrant designs a rating scale distinct from that of the incumbent. It targets higher-than-average companies in each rating grade of the incumbent\u27s rating scale and employs more stringent rating standards. We use Standard and Poor\u27s (S&P) entry into the market for insurance ratings previously covered by a monopolist, A.M. Best, to empirically test the impact of entry on the information content of ratings. The empirical analysis reveals that S&P required higher standards to assign a rating similar to the one assigned by A.M. Best and that higher-than-average quality insurers in each rating category of A.M. Best chose to receive a second rating from S&P

Management Options of Colonoscopic Splenic Injury

Injury to the spleen during routine colonoscopy is an extremely rare injury. Diagnosis and management of the injury has evolved with technological advances and experience gained in the management of splenic injuries sustained in trauma. Of the 37 reported cases of colonoscopic splenic injury, 12 had a history of prior surgery or a disease process suggesting the presence of adhesions. Only 6 had noted difficulty during the procedure, and 31 patients experienced pain, shock, or hemoglobin drop as the indication of splenic injury. Since 1989, 21/24 (87.5%) patients have been diagnosed initially using computed tomography or ultrasonography. Overall, only 27.8% have retained their spleens. None have experienced as long a delay as our patient, nor have any had an attempt at percutaneous control of the injury. This report presents an unusual case of a rare complication of colonoscopy and the unsuccessful use of one nonoperative technique, and reviews the experience reported in the world literature, including current day management options