Experimenter's Freedom in Bell's Theorem and Quantum Cryptography

Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the violation of Bell's inequalities can only be understood if this freedom is denied. We determine the minimal degree to which the experimenter's freedom has to be abandoned, if one wants to keep such a picture and be in agreement with the experiment. Furthermore, the freedom in choosing experimental arrangements may be considered as a resource, since its lacking can be used by an eavesdropper to harm the security of quantum communication. We analyze the security of quantum key distribution as a function of the (partial) knowledge the eavesdropper has about the future choices of measurement settings which are made by the authorized parties (e.g. on the basis of some quasi-random generator). We show that the equivalence between the violation of Bell's inequality and the efficient extraction of a secure key - which exists for the case of complete freedom (no setting knowledge) - is lost unless one adapts the bound of the inequality according to this lack of freedom.Comment: 7 pages, 2 figures, incorporated referee comment

Addressing the clumsiness loophole in a Leggett-Garg test of macrorealism

The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a "Bell inequality in time" designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The "clumsiness" loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller "collusion" loophole.Comment: 7 pages, 3 figure

Design of a scalable, single-use photobioreactor for the growth of algae in axenic conditions

University of Technology Sydney. Faculty of Science.Microalgal cultivation systems for biopharmaceutical production are currently limited and current biopharmaceutical bioreactors are not optimized in terms of efficient light and substrate supply for algae. This project aims to address this gap, by establishing a process to convert and optimize a bioreactor system which is already established in the biopharmaceutical sector into a photo-bioreactor (PBR) system, facilitating axenic microalgae growth at an industrial scale in a regulated environment. The system to be converted is an industrially used single-use bioreactor, for which an optimization platform was designed including both physical and digital components. The physical part consisted of a 200 L PBR and a scaled down 20 L PBR, both mimicking physical characteristics of the industrial bioreactor, thereby enabling the rapid testing of new illumination systems. Different methods, such as gassing-in method (mass transfer), pH- and dye-method (mixing time) and optical particle tracing (hydrodynamic flow) were utilized to characterise the system and validate the down-scaling process, which revealed similar cultivation features compared to the industrial bioreactor. The predominant focus of the optimization platform was the supply of light: as such, accurate and precise data of the light attenuation were needed. A novel, practical, and easily applicable optical method using modified cameras for measuring the light distribution of complex light sources was developed to address this – Direct Chlorophyll Fluorescence Imaging (DCFI). DCFI was applied to and cultures at different cell concentrations for a variety of LED wavelengths, yielding precise light maps of the light distribution into the culture. These light maps and the particle tracing data were combined in a computer aided design (CAD) process which enabled the calculation of the best configuration of the artificial light system (LEDs) according to the optimal light experience for the microalgae cells. The CAD forms the digital component of the optimization platform and completes the system. The optimization platform and the underlying methodology builds the foundation for a streamlined approach to convert existing bioreactor systems or to optimize alternative PBR systems. As such, this technology can help in establishing microalgae as a cultivation system in the biopharmaceutical sector

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Free randomness can be amplified

Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. However, these results are based on the assumption that measurement settings can be chosen freely at random, so assume the existence of perfectly free random processes from the outset. Here we consider a scenario in which this assumption is weakened and show that partially free random bits can be amplified to make arbitrarily free ones. More precisely, given a source of random bits whose correlation with other variables is below a certain threshold, we propose a procedure for generating fresh random bits that are virtually uncorrelated with all other variables. We also conjecture that such procedures exist for any non-trivial threshold. Our result is based solely on the no-signalling principle, which is necessary for the existence of free randomness.Comment: 5+7 pages, 2 figures. Updated to match published versio

Severe depletion of mitochondrial DNA in spinal muscular atrophy

Spinal muscular atrophy (SMA) is a neuromus- cular disorder in childhood leading to a dramatic loss of muscle strength. Functional investigations with high-reso- lution polarography and enzyme measurements of the res- piratory chain revealed lowered activities in muscle tissue of SMA patients. To gain a better understanding of this low energy supply we analyzed the amount of mitochon- drial DNA (mtDNA) in skeletal muscle of 20 unrelated children with genetically proven SMA and 31 controls. Quantitative Southern blot analysis revealed a severe and homogeneous decrease in the content of muscle mtDNA in relation to nuclear DNA in SMA patients (90.3±7.8%), whereas by immunofluorescence no decrease in the num- ber of mitochondria was detected. In addition, a two- to threefold reduction of the nuclear-encoded complex II (succinate dehydrogenase) activity was detected in SMA muscle tissue. Western blot analysis showed a significant reduction of both mitochondrial- and nuclear-encoded cy- tochrome c oxidase subunits. Our results indicate that mtDNA depletion in SMA is a consequence of severe at- rophy, and has to be differentiated by measurement of complex II from an isolated reduction of mtDNA as found in patients with mitochondriocytopathies and the so- called mtDNA depletion syndrome