Aspects of mutually unbiased bases in odd prime power dimensions

We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the cyclic group $G$ of order $p$. This form may be useful in explicitly writing down mutually unbiased bases for $N=p^r$.Comment: 3 pages, latex, no figure

Beyond Activation: Characterizing Microglial Functional Phenotypes

Classically, the following three morphological states of microglia have been defined: ramified, amoeboid and phagocytic. While ramified cells were long regarded as “resting”, amoeboid and phagocytic microglia were viewed as “activated”. In aged human brains, a fourth, morphologically novel state has been described, i.e., dystrophic microglia, which are thought to be senescent cells. Since microglia are not replenished by blood-borne mononuclear cells under physiological circumstances, they seem to have an “expiration date” limiting their capacity to phagocytose and support neurons. Identifying factors that drive microglial aging may thus be helpful to delay the onset of neurodegenerative diseases, such as Alzheimer’s disease (AD). Recent progress in single-cell deep sequencing methods allowed for more refined differentiation and revealed regional-, age- and sex-dependent differences of the microglial population, and a growing number of studies demonstrate various expression profiles defining microglial subpopulations. Given the heterogeneity of pathologic states in the central nervous system, the need for accurately describing microglial morphology and expression patterns becomes increasingly important. Here, we review commonly used microglial markers and their fluctuations in expression in health and disease, with a focus on IBA1 low/negative microglia, which can be found in individuals with liver disease

Reduced randomness in quantum cryptography with sequences of qubits encoded in the same basis

We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.Comment: 8 pages, submitted to PR

Dystrophic (senescent) rather than activated microglial cells are associated with tau pathology and likely precede neurodegeneration in Alzheimer’s disease

The role of microglial cells in the pathogenesis of Alzheimer’s disease (AD) neurodegeneration is unknown. Although several works suggest that chronic neuroinflammation caused by activated microglia contributes to neurofibrillary degeneration, anti-inflammatory drugs do not prevent or reverse neuronal tau pathology. This raises the question if indeed microglial activation occurs in the human brain at sites of neurofibrillary degeneration. In view of the recent work demonstrating presence of dystrophic (senescent) microglia in aged human brain, the purpose of this study was to investigate microglial cells in situ and at high resolution in the immediate vicinity of tau-positive structures in order to determine conclusively whether degenerating neuronal structures are associated with activated or with dystrophic microglia. We used a newly optimized immunohistochemical method for visualizing microglial cells in human archival brain together with Braak staging of neurofibrillary pathology to ascertain the morphology of microglia in the vicinity of tau-positive structures. We now report histopathological findings from 19 humans covering the spectrum from none to severe AD pathology, including patients with Down’s syndrome, showing that degenerating neuronal structures positive for tau (neuropil threads, neurofibrillary tangles, neuritic plaques) are invariably colocalized with severely dystrophic (fragmented) rather than with activated microglial cells. Using Braak staging of Alzheimer neuropathology we demonstrate that microglial dystrophy precedes the spread of tau pathology. Deposits of amyloid-beta protein (Aβ) devoid of tau-positive structures were found to be colocalized with non-activated, ramified microglia, suggesting that Aβ does not trigger microglial activation. Our findings also indicate that when microglial activation does occur in the absence of an identifiable acute central nervous system insult, it is likely to be the result of systemic infectious disease. The findings reported here strongly argue against the hypothesis that neuroinflammatory changes contribute to AD dementia. Instead, they offer an alternative hypothesis of AD pathogenesis that takes into consideration: (1) the notion that microglia are neuron-supporting cells and neuroprotective; (2) the fact that development of non-familial, sporadic AD is inextricably linked to aging. They support the idea that progressive, aging-related microglial degeneration and loss of microglial neuroprotection rather than induction of microglial activation contributes to the onset of sporadic Alzheimer’s disease. The results have far-reaching implications in terms of reevaluating current treatment approaches towards AD

Quantum Cryptography using larger alphabets

Like all of quantum information theory, quantum cryptography is traditionally based on two level quantum systems. In this letter, a new protocol for quantum key distribution based on higher dimensional systems is presented. An experimental realization using an interferometric setup is also proposed. Analyzing this protocol from the practical side, one finds an increased key creation rate while keeping the initial laser pulse rate constant. Analyzing it for the case of intercept/resend eavesdropping strategy, an increased error rate is found compared to two dimensional systems, hence an advantage for the legitimate users to detect an eavesdropper.Comment: 12 pages, 2 (eps) figure

Optimal eavesdropping in cryptography with three-dimensional quantum states

We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.Comment: 4 pages, 2 figure