Preparation and Measurement Uncertainty in Quantum Mechanics

This thesis addresses two forms of quantum uncertainty. In part I, we focus on preparation uncertainty, an expression of the fact that there are sets of observables for which the induced probability distributions are not simultaneously sharp in any state. We exactly characterise the preparation uncertainty regions for several finite dimensional case studies, including a new derivation of the preparation uncertainty region for the Pauli observables of qubits, and two qutrit case studies which have not previously been addressed in the literature. We also consider the variance based preparation uncertainty for position and momentum observables for the well known “particle in a box” system. We see that the appropriate momentum observable is not given by the spectral measure of a self-adjoint operator, although the position observable is. The box system lacks the phase-space symmetry used to determine the free particle and particle on a ring systems so determining the box uncertainty region is rather more difficult than in these cases. We give upper and lower bounds on the boundary of the uncertainty region, and show that our upper bound is exact in an interval. In part II we turn our attention to measurement uncertainty, exploring the space of compatible joint approximations to incompatible target observables. We prove a general theorem, which shows that, for a broad class of figures of merit, the optimal compatible approximations to covariant targets are themselves covariant. This substantially simplifies the problem of determining measurement uncertainty regions for covariant observables, since the space of covariant compatible approximations is smaller than the space of all compatible approximations. We employ this theorem to derive measurement uncertainty regions for three mutually orthogonal Pauli observables, and for the quantum Fourier pair acting in any finite dimension

Fast estimation of outcome probabilities for quantum circuits

We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each other by performing best in different parameter regimes. The $\tt{Estimate}$ algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like $\approx 1.17^t$ for $T$ gates). Our algorithm is state-of-the-art for this task: as an example, in approximately $13$ hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of $0.03$, for a $50$ qubit, $60$ non-Clifford gate quantum circuit with more than $2000$ Clifford gates. Our second algorithm, $\tt{Compute}$, calculates the probability of a chosen measurement outcome to machine precision with run-time $O(2^{t-r} t)$ where $r$ is an efficiently computable, circuit-specific quantity. With high probability, $r$ is very close to $\min \{t,n-w\}$ for random circuits with many Clifford gates, where $w$ is the number of measured qubits. $\tt{Compute}$ can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+$T$ circuits with $n=55$, $w=5$, $c=10^5$ and $t=80$ $T$ gates, and then compute the Born rule probability with a run-time consistently less than $10$ minutes using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms.Comment: 25+14 pages, 6 figures. Version 2 contains a minor correction to the scaling of Theorem 3, a small improvement to the scaling of Theorem 2 and various other improvements. Comments welcom

When the Wealthy Are Poor: Poverty Explanations and Local Perspectives in Southwestern Madagascar

To reduce poverty, one must understand what poverty means in local contexts. We used focus groups to elicit a “folk model” of poverty from Masikoro, Vezo, and Mikea people in rural southwestern Madagascar and then placed this model in dialogue with four social science models: economic growth, substantivism, mode of production, and livelihoods. The folk model emphasizes household continuity, production of people, and exploitative expropriation by the wealthy. Absent from the folk model is scarcity of natural and social resources, the core of economic growth and livelihoods explanations. Consistent with substantivism, poverty and wealth are states one may occupy simultaneously, not maximizable quantities. Compatible with mode of production, the root cause of poverty is the rules regarding control over property. Poverty interventions based on profit, competition, intensification, or devolution of control to traditional social institutions would likely be culturally foreign to rural Malagasy and could further the gap between rich and poor

Proteomics of Buccal Cavity Mucus in Female Tilapia Fish (Oreochromis spp.): A Comparison between Parental and Non-Parental Fish

Mouthbrooding is an elaborate form of parental care displayed by many teleost species. While the direct benefits of mouthbrooding such as protection and transportation of offsprings are known, it is unclear if mouthbrooding offers additional benefits to embryos during incubation. In addition, mouthbrooding could incur negative costs on parental fish, due to limited feeding opportunities. Parental tilapia fish (Oreochromis spp.) display an elaborated form of parental care by incubating newly hatched embryos in oral buccal cavity until the complete adsorption of yolk sac. In order to understand the functional aspects of mouthbrooding, we undertake a proteomics approach to compare oral mucus sampled from mouthbrooders and non-mouthbrooders, respectively. Majority of the identified proteins have also been previously identified in other biological fluids or mucus-rich organs in different organisms. We also showed the upregulation of 22 proteins and down regulation of 3 proteins in mucus collected from mouthbrooders. Anterior gradient protein, hemoglobin beta-A chain and alpha-2 globin levels were lower in mouthbrooder samples. Mouthbrooder oral mucus collectively showed increase levels of proteins related to cytoskeletal properties, glycolytic pathway and mediation of oxidative stress. Overall the findings suggest cellular stress response, probably to support production of mucus during mouthbrooding phase

Integrated genomic characterization of pancreatic ductal adenocarcinoma

We performed integrated genomic, transcriptomic, and proteomic profiling of 150 pancreatic ductal adenocarcinoma (PDAC) specimens, including samples with characteristic low neoplastic cellularity. Deep whole-exome sequencing revealed recurrent somatic mutations in KRAS, TP53, CDKN2A, SMAD4, RNF43, ARID1A, TGFβR2, GNAS, RREB1, and PBRM1. KRAS wild-type tumors harbored alterations in other oncogenic drivers, including GNAS, BRAF, CTNNB1, and additional RAS pathway genes. A subset of tumors harbored multiple KRAS mutations, with some showing evidence of biallelic mutations. Protein profiling identified a favorable prognosis subset with low epithelial-mesenchymal transition and high MTOR pathway scores. Associations of non-coding RNAs with tumor-specific mRNA subtypes were also identified. Our integrated multi-platform analysis reveals a complex molecular landscape of PDAC and provides a roadmap for precision medicine