Tightening Quantum Speed Limits for Almost All States

Conventional quantum speed limits perform poorly for mixed quantum states: They are generally not tight and often significantly underestimate the fastest possible evolution speed. To remedy this, for unitary driving, we derive two quantum speed limits that outperform the traditional bounds for almost all quantum states. Moreover, our bounds are significantly simpler to compute as well as experimentally more accessible. Our bounds have a clear geometric interpretation; they arise from the evaluation of the angle between generalized Bloch vectors.Comment: Updated and revised version; 5 pages, 2 figures, 1 page appendi

Tomographically reconstructed master equations for any open quantum dynamics

Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.Comment: 10+4 pages, 5 figure

Non-thermal radiation from molecular clouds illuminated by cosmic rays from nearby supernova remnants

Molecular clouds are expected to emit non-thermal radiation due to cosmic ray interactions in the dense magnetized gas. Such emission is amplified if a cloud is located close to an accelerator of cosmic rays and if cosmic rays can leave the accelerator and diffusively reach the cloud. We consider the situation in which a molecular cloud is located in the proximity of a supernova remnant which is accelerating cosmic rays and gradually releasing them into the interstellar medium. We calculate the multiwavelength spectrum from radio to gamma rays which emerges from the cloud as the result of cosmic ray interactions. The total energy output is dominated by the gamma ray emission, which can exceed the emission from other bands by an order of magnitude or more. This suggests that some of the unidentified TeV sources detected so far, with no obvious or very weak counterpart in other wavelengths, might be associated with clouds illuminated by cosmic rays coming from a nearby source.Comment: 4 pages, 3 figures, proceedings of the "4th Heidelberg International Symposium on High Energy Gamma-Ray Astronomy" July 7-11, 2008, Heidelberg, German

On the Regularized Fermionic Projector of the Vacuum

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional ${\mathcal{M}} P$-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.Comment: 66 pages, LaTeX, 8 figures, minor improvements (published version

An introduction to operational quantum dynamics

In the summer of 2016, physicists gathered in Torun, Poland for the 48th annual Symposium on Mathematical Physics. This Symposium was special; it celebrated the 40th anniversary of the discovery of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in quantum physics and quantum chemistry. This article forms part of a Special Volume of the journal Open Systems & Information Dynamics arising from that conference; and it aims to celebrate a related discovery -- also by Sudarshan -- that of Quantum Maps (which had their 55th anniversary in the same year). Nowadays, much like the master equation, quantum maps are ubiquitous in physics and chemistry. Their importance in quantum information and related fields cannot be overstated. In this manuscript, we motivate quantum maps from a tomographic perspective, and derive their well-known representations. We then dive into the murky world beyond these maps, where recent research has yielded their generalisation to non-Markovian quantum processes.Comment: Submitted to Special OSID volume "40 years of GKLS

Multiple Parameter Estimation With Quantized Channel Output

We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival (DOA) estimation). The work is of interest in the case when low resolution A/D-converters (ADCs) have to be used to enable higher sampling rate and to simplify the hardware. An Expectation-Maximization (EM) based algorithm is proposed for solving this problem in a general setting. Besides, we derive the Cramer-Rao Bound (CRB) and discuss the effects of quantization and the optimal choice of the ADC characteristic. Numerical and analytical analysis reveals that reliable estimation may still be possible even when the quantization is very coarse.Comment: 9 pages, 9 figures, International ITG Workshop on Smart Antennas - WSA 2010, Bremen, German

Do the low PN velocity dispersions around elliptical galaxies imply that these lack dark matter?

While kinematical modelling of the low PN velocity dispersions observed in the outer regions of elliptical galaxies suggest a lack of dark matter around these galaxies, we report on an analysis of a suite of $N$-body simulations (with gas) of major mergers of spiral galaxies embedded in dark matter halos, and find that the outer velocity dispersions are as low as observed for the PNe. The inconsistency between our dynamical modelling and previous kinematical modelling is caused by very radial stellar orbits and projection effects when viewing face-on oblate ellipticals. Our simulations (weakly) suggest the youth of PNe around ellipticals, and we propose that the universality of the PN luminosity function may be explained if the bright PNe in ellipticals are formed after the regular accretion of very low mass gas-rich galaxies.Comment: Contributed talk at meeting, "Planetary Nebulae as astronomical tools", Gdansk, Poland, June-July 2005, ed. R. Szczerba, G. Stasi\'nska, and S. K. G\'orny, AIP Conference Proceedings, Melville, New York, 2005. 4 or 5 pages, 6 figure