Theory of Quantum Pulse Position Modulation and Related Numerical Problems

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find optimal (or suboptimal) measurement operators and to evaluate the corresponding error probability. For PPM, the correct formulation of quantum states is given by the tensorial product of m identical Hilbert spaces, where m is the PPM order. The presence of mixed states, due to thermal noise, generates an optimization problem involving matrices of huge dimensions, which already for 4-PPM, are of the order of ten thousand. To overcome this computational complexity, the currently available methods of quantum detection, which are based on explicit results, convex linear programming and square root measurement, are compared to find the computationally less expensive one. In this paper a fundamental role is played by the geometrically uniform symmetry of the quantum PPM format. The evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart.Comment: 10 pages, 7 figures, accepted for publication in IEEE Trans. on Communication

A nanometer-scale optical electrometer

Self-assembled semiconductor quantum dots show remarkable optical and spin coherence properties, which have lead to a concerted research effort examining their potential as a quantum bit for quantum information science1-6. Here, we present an alternative application for such devices, exploiting recent achievements of charge occupation control and the spectral tunability of the optical emission of quantum dots by electric fields7 to demonstrate high-sensitivity electric field measurement. In contrast to existing nanometer-scale electric field sensors, such as single electron transistors8-11 and mechanical resonators12,13, our approach relies on homodyning light resonantly Rayleigh scattered from a quantum dot transition with the excitation laser and phase sensitive lock-in detection. This offers both static and transient field detection ability with high bandwidth operation and near unity quantum efficiency. Our theoretical estimation of the static field sensitivity for typical parameters, 0.5 V/m/ \surd Hz, compares favorably to the theoretical limit for single electron transistor-based electrometers. The sensitivity level of 5 V/m/ \surd Hz we report in this work, which corresponds to 6.4 * 10-6 e/ \surd Hz at a distance of 12 nm, is worse than this theoretical estimate, yet higher than any other result attained at 4.2 K or higher operation temperature

Gaussian states and geometrically uniform symmetry

Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform symmetry, a property of quantum states that greatly simplifies the derivation of the optimal decision by means of the square root measurements. In a general framework of the $N$-mode Gaussian states we show the general properties of this symmetry and the application of the optimal quantum measurements. An application example is presented, to quantum communication systems employing pulse position modulation. We prove that the geometrically uniform symmetry can be applied to the general class of multimode Gaussian states

Numerical Optical Centroid Measurements

Optical imaging methods are typically restricted to a resolution of order of the probing light wavelength $\lambda_p$ by the Rayleigh diffraction limit. This limit can be circumvented by making use of multiphoton detection of correlated $N$-photon states, having an effective wavelength $\lambda_p/N$. But the required $N$-photon detection usually renders these schemes impractical. To overcome this limitation, recently, so-called optical centroid measurements (OCM) have been proposed which replace the multi-photon detectors by an array of single-photon detectors. Complementary to the existing approximate analytical results, we explore the approach using numerical experiments by sampling and analyzing detection events from the initial state wave function. This allows us to quantitatively study the approach also beyond the constraints set by the approximate analytical treatment, to compare different detection strategies, and to analyze other classes of input states.Comment: 15 pages, 18 figure