Quantum Memristors in Quantum Photonics

We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that this tunable beam splitter, when equipped with weak measurements and classical feedback, behaves as a quantum memristor. Indeed, in order to prove its quantumness, we show how to codify quantum information in the coherent beams. Moreover, we estimate the memory capability of the quantum memristor. Finally, we show the feasibility of the proposed setup in integrated quantum photonics

Genus and spot density in the COBE DMR first year anisotropy maps

A statistical analysis of texture on the {\it COBE}-DMR first year sky maps based on the genus and spot number is presented. A generalized $\chi^2$ statistic is defined in terms of ``observable'' quantities: the genus and spot density that would be measured by different cosmic observers. This strategy together with the use of Monte Carlo simulations of the temperature fluctuations, including all the relevant experimental parameters, represent the main difference with previous analyses. Based on the genus analysis we find a strong anticorrelation between the quadrupole amplitude $Q_{rms-PS}$ and the spectral index $n$ of the density fluctuation power spectrum at recombination of the form $Q_{rms-PS}= 22.2 \pm 1.7 - (4.7 \pm 1.3) \times n\ \mu$K for fixed $n$, consistent with previous works. The result obtained based on the spot density is consistent with this $Q_{rms-PS} (n)$ relation. In addition to the previous results we have determined, using Monte Carlo simulations, the minimum uncertainty due to cosmic variance for the determination of the spectral index with the genus analysis. This uncertainty is $\delta n\approx 0.2$.Comment: 5 pages, uuencode file containing text and 1 figure. MNRAS in press