Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements

In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit undergoes at most $D$ diagonal gates, (iii) each qudit is destructively measured in the computational basis or bases unbiased to it, and (iv) each qudit is initialised within $\lambda^{-D}$ of a diagonal state according to a particular distance measure. In this work we explicitly compute $\lambda$ for any two qubit diagonal gate, thereby extending the computation of arXiv:2201.07655v2 beyond CZ gates. For any finite degree graph this allows us to describe a two parameter family of pure entangled quantum states (or three parameter family of thermal states) which have a non-trivial classically efficiently simulatable "phase" for the permitted measurements, even though other values of the parameters may enable ideal cluster state quantum computation. The main the technical tool involves considering separability in terms of "cylindrical" sets of operators. We also consider whether a different choice of set can strengthen the algorithm, and prove that they are optimal among a broad class of sets, but also show numerically that outside this class there are choices that can increase the size of the classically efficient regime.Comment: 12 pages, 3 figure

Physical layer security solutions against passive and colluding eavesdroppers in large wireless networks and impulsive noise environments

Wireless networks have experienced rapid evolutions toward sustainability, scalability and interoperability. The digital economy is driven by future networked societies to a more holistic community of intelligent infrastructures and connected services for a more sustainable and smarter society. Furthermore, an enormous amount of sensitive and confidential information, e.g., medical records, electronic media, financial data, and customer files, is transmitted via wireless channels. The implementation of higher layer key distribution and management was challenged by the emergence of these new advanced systems. In order to resist various malicious abuses and security attacks, physical layer security (PLS) has become an appealing alternative. The basic concept behind PLS is to exploit the characteristics of wireless channels for the confidentiality. Its target is to blind the eavesdroppers such that they cannot extract any confidential information from the received signals. This thesis presents solutions and analyses to improve the PLS in wireless networks. In the second chapter, we investigate the secrecy capacity performance of an amplify-andforward (AF) dual-hop network for both distributed beamforming (DBF) and opportunistic relaying (OR) techniques. We derive the capacity scaling for two large sets; trustworthy relays and untrustworthy aggressive relays cooperating together with a wire-tapper aiming to intercept the message. We show that the capacity scaling in the DBF is lower bounded by a value which depends on the ratio between the number of the trustworthy and the untrustworthy aggressive relays, whereas the capacity scaling of OR is upper bounded by a value depending on the number of relays as well as the signal to noise ratio (SNR). In the third chapter, we propose a new location-based multicasting technique, for dual phase AF large networks, aiming to improve the security in the presence of non-colluding passive eavesdroppers. We analytically demonstrate that the proposed technique increases the security by decreasing the probability of re-choosing a sector that has eavesdroppers, for each transmission time. Moreover, we also show that the secrecy capacity scaling of our technique is the same as for broadcasting. Hereafter, the lower and upper bounds of the secrecy outage probability are calculated, and it is shown that the security performance is remarkably enhanced, compared to the conventional multicasting technique. In the fourth chapter, we propose a new cooperative protocol, for dual phase amplify-andforward large wireless sensor networks, aiming to improve the transmission security while taking into account the limited capabilities of the sensor nodes. In such a network, a portion of the K relays can be potential passive eavesdroppers. To reduce the impact of these untrustworthy relays on the network security, we propose a new transmission protocol, where the source agrees to share with the destination a given channel state information (CSI) of source-trusted relay-destination link to encode the message. Then, the source will use this CSI again to map the right message to a certain sector while transmitting fake messages to the other sectors. Adopting such a security protocol is promising because of the availability of a high number of cheap electronic sensors with limited computational capabilities. For the proposed scheme, we derived the secrecy outage probability (SOP) and demonstrated that the probability of receiving the right encoded information by an untrustworthy relay is inversely proportional to the number of sectors. We also show that the aggressive behavior of cooperating untrusted relays is not effective compared to the case where each untrusted relay is trying to intercept the transmitted message individually. Fifth and last, we investigate the physical layer security performance over Rayleigh fading channels in the presence of impulsive noise, as encountered, for instance, in smart grid environments. For this scheme, secrecy performance metrics were considered with and without destination assisted jamming at the eavesdropper’s side. From the obtained results, it is verified that the SOP, without destination assisted jamming, is flooring at high signal-to-noise-ratio values and that it can be significantly improved with the use of jamming

The Wintertime Southern Hemisphere Split Jet: Structure, Variability, and Evolution

A persistent feature of the Southern Hemisphere upper-level time-mean flow is the presence of a split jet across the South Pacific east of Australia during the austral winter. The split jet is composed of the subtropical jet (STJ) on its equatorward branch and the polar front jet (PFJ) on its poleward branch. The NCEP-NCAR reanalysis is used to investigate the structure and evolution of the split jet. Results show that the presence/absence of the PFJ determines the degree of split flow, given that the STJ is a quasi-steady feature. A split-flow index (SFI) is developed to quantify the variability of the split jet, in which negative values represent strong split flow and positive values nonsplit flow. Correlations with teleconnection indices are investigated, with the SFI positively correlated to the Southern Oscillation index and negatively correlated to the Antarctic oscillation. The SFI is used to construct composites of heights, temperature, and wind for split-flow and non-split-flow days. The composites reveal that relatively cold conditions occur in the South Pacific in association with non-split-flow regimes, and split-flow regimes occur when relatively warm conditions prevail. In the latter situation cold air bottled up over Antarctica helps to augment the background tropospheric thickness gradient between Antarctica and the lower latitudes with a resulting increase in the thermal wind and the PFJ. It is surmised that frequent cold surges out of Antarctica moving into the South Pacific are associated with non-split-flow regimes. In this context, the variability of the split jet responds to large-scale baroclinic processes and is further modulated by synoptic-scale disturbances

Quantitative expression of oestrogen receptor in breast cancer: Clinical and molecular significance

BackgroundOestrogen receptor (ER) positive breast cancer (BC) patients are eligible for endocrine therapy (ET), regardless of ER immunohistochemical expression level. There is a wide spectrum of ER expression and the response to ET is not uniform. This study aimed to assess the clinical and molecular consequences of ER heterogeneity with respect to ET-response.MethodsER expression, categorised by percentage and staining intensity in a large BC cohort (n = 7559) was correlated with clinicopathological parameters and patient ET response. The Cancer Genome Atlas Data BC cohort (n = 1047) was stratified by ER expression and transcriptomic analysis completed to better understand the molecular basis of ER heterogeneity.ResultsThe quantitative proportional increase in ER expression was positively associated with favourable prognostic parameters. Tumours with 1–9% ER expression were characteristically similar to ER-negative (<1%) tumours. Maximum ET-response was observed in tumours with 100% ER expression, with responses significantly different to tumours exhibiting ER at < 100% and significantly decreased survival rates were observed in tumours with 50% and 10% of ER expression. The Histochemical-score (H-score), which considers both staining intensity and percentage, added significant prognostic value over ER percentage alone with significant outcome differences observed at H-scores of 30, 100 and 200. There was a positive correlation between ER expression and ESR1 mRNA expression and expression of ER-regulated genes. Pathway analysis identified differential expression in key cancer-related pathways in different ER-positive groups.ConclusionET-response is statistically proportionally related to ER expression with significant differences observed at 10%, 50% and 100%. The H-score adds prognostic and predictive information

Improved Adaptive Group Testing Algorithms with Applications to Multiple Access Channels and Dead Sensor Diagnosis

We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the defective items in a set of items when we can test arbitrary subsets of items. In the standard group-testing problem, the result of a test is binary--the tested subset either contains defective items or not. In the more generalized versions we study in this paper, the result of each test is non-binary. For example, it may indicate whether the number of defective items contained in the tested subset is zero, one, or at least two. We give adaptive algorithms that are provably more efficient than previous group testing algorithms. We also show how our algorithms can be applied to solve conflict resolution on a MAC and dead sensor diagnosis. Dead sensor diagnosis poses an interesting challenge compared to MAC resolution, because dead sensors are not locally detectable, nor are they themselves active participants.Comment: Expanded version of a paper appearing in ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), and preliminary version of paper appearing in Journal of Combinatorial Optimizatio