לוח שנה משולב

The talk is based on Nicolas Bergeron’s book, Sections 5.1–5.2.

Let C be an error-correcting code over a large alphabet q of block length n, and assume that a possibly corrupted codeword c is distributively stored among n servers where the ith entry is being held by the ith server. Suppose that every pair of servers publicly announce whether the corresponding coordinates are ``consistent'' with some legal codeword or ``conflicted''. What type of information about c can be inferred from this consistency graph? Can we check whether errors occurred and if so, can we find the error locations and effectively decode? We initiate the study of conflict-checkable and conflict-decodable codes and prove the following main results:

(1) (Almost-MDS conflict-checkable codes:) For every distance d = n-d 0.99. Interestingly, the code is non-linear, and we give some evidence that suggests that this is inherent. Combinatorially, this yields an n-partite graph over [q]^n that contains q^k cliques of size n whose pairwise intersection is at most n-d

While colloidal quantum dots (CQDs) are already an important building block in electro-optical devices, in the realm of quantum science and technology, they are often considered inferior with respect to emitters such as solid-state defects and epitaxial quantum dots. Despite their single-photon emission [1], demonstrations of quantum coherence and control are largely still lacking. The main obstacle towards these is spectral diffusion – stochastic fluctuations in the energy of photons emitted from an individual CQD even at cryogenic temperatures. In this talk, I will present our recent work providing, for the first time, direct and definitive proof that these fluctuations arise from stochastic electric fields in the particle’s nano environment [2]. However, the high sensitivity of CQDs to electric fields, through the quantum-confined Stark effect, can also be perceived as a feature, rather than a bug. I will present future concepts for coherent control of a single photon’s temporal wavefunction through an electric bias. Relying on tools from the terahertz and femtosecond-laser toolboxes [3,4], spectroscopy and control at fast-to-ultrafast (millisecond-to-femtosecond) timescales, will play a detrimental role in fulfilling the unique potential that CQDs hold in the field of quantum optics,.
[1] R. Tenne, U. Rossman, B. Rephael, Y. Israel, A. Krupinski-Ptaszek, R. Lapkiewicz, Y. Silberberg, and D. Oron, Super-Resolution Enhancement by Quantum Image Scanning Microscopy, Nature Photonics 13, 116 (2019).
[2] F. Conradt, V. Bezold, V. Wiechert, S. Huber, S. Mecking, A. Leitenstorfer, and R. Tenne, Electric-Field Fluctuations as the Cause of Spectral Instabilities in Colloidal Quantum Dots, Nano Lett. 23, 9753 (2023).
[3] P. Henzler et al., Femtosecond Transfer and Manipulation of Persistent Hot-Trion Coherence in a Single CdSe/ZnSe Quantum Dot, Physical Review Letters 126, 067402 (2021).
[4] P. Fischer, G. Fitzky, D. Bossini, A. Leitenstorfer, and R. Tenne, Quantitative Analysis of Free-Electron Dynamics in InSb by Terahertz Shockwave Spectroscopy, Physical Review B 106, 205201 (2022).

Reported cases of diarrheal samples exhibiting co-infections or multiple infections with two or more infectious agents are on the rise, likely due to advances in bacterial diagnostic techniques. Our work aims to decode the communication between bacterial pathogens within the digestive system and investigates whether they compete or cooperate. Additionally, we examine how commensal strains of the microbiome intercept this communication through specific metabolites

The talk is based on Nicolas Bergeron’s book, Section 5.4.