Quantum elimination measurements

If an initial state is prepared from a known set, then the aim of a quantum state elimination measurement is to rule out a subset of the possible initial states. We use semi-definite programming to find either bounds or exact results on the success probabilities of certain elimination measurements. In conjunction we use an analytic approach to find optimal measurements. We obtain optimal measurements for unambiguous elimination in a two-qubit case where each qubit is in one of two possible states. We also show how it might be possible to use our elimination measurements in a QKD protocol. In addition we prove that the best method to eliminate the highest average number of states for sequences of qubits with each qubit in one of two possible states is individual unambiguous measurements. Furthermore we show the method of decomposing a unitary matrix into beamsplitter-like operations found by Reck et al. and apply this to our elimination measurement to realise a way of experimental implementation. In the final chapter we look at joint measurements and find the optimal probe state that we would use to minimise the uncertainty in our estimation of the sharpness of a measurement between two observables.Engineering and Physical Sciences Research Council (EPSRC) funding

Effect of component variations on the gate fidelity in linear optical networks

We investigate the effect of variations in beam-splitter transmissions and path-length differences in the nonlinear sign gate that is used for linear optical quantum computing. We identify two implementations of the gate and show that the sensitivity to variations in their components differs significantly between them. Therefore, circuits that require a precision implementation will generally benefit from additional circuit analysis of component variations to identify the most practical implementation. We suggest possible routes to efficient circuit analysis in terms of quantum parameter estimation

Unambiguous quantum state elimination for qubit sequences

Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is rather than what it is not. Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography. We consider unambiguous quantum state elimination for two or more qubits, where each qubit can be in one of two possible states. Optimal measurements for eliminating one and two states out of four two-qubit states are given. We also prove that if we want to maximize the average number of eliminated overall N -qubit states, then individual measurements on each qubit are optimal

Optimal simultaneous measurements of incompatible observables of a single photon

The ultimate limits of measurement precision are dictated by the laws of quantum mechanics. One of the most fascinating results is that joint or simultaneous measurements of noncommuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for determining what an “optimal” joint measurement is, with corresponding different trade-off relations for the measurements. It is generally a nontrivial task to devise or implement a strategy that minimizes the joint-measurement uncertainty. Here, we implement the simplest possible technique for an optimal four-outcome joint measurement and demonstrate a type of optimal measurement that has not been realized before in a photonic setting. We experimentally investigate a joint-measurement uncertainty relation that is more fundamental in the sense that it refers only to probabilities and is independent of values assigned to measurement outcomes. Using a heralded single-photon source, we demonstrate quantum-limited performance of the scheme on single quanta. Since quantum measurements underpin many concepts in quantum information science, this study is both of fundamental interest and relevant for emerging photonic quantum technologies

A generative network model of neurodevelopmental diversity in structural brain organization

Funder: RCUK | Medical Research Council (MRC); doi: https://doi.org/10.13039/501100000265Funder: James S. McDonnell Foundation (McDonnell Foundation); doi: https://doi.org/10.13039/100000913Funder: Cambridge Commonwealth, European and International Trust (Cambridge Commonwealth, European & International Trust); doi: https://doi.org/10.13039/501100003343Abstract: The formation of large-scale brain networks, and their continual refinement, represent crucial developmental processes that can drive individual differences in cognition and which are associated with multiple neurodevelopmental conditions. But how does this organization arise, and what mechanisms drive diversity in organization? We use generative network modeling to provide a computational framework for understanding neurodevelopmental diversity. Within this framework macroscopic brain organization, complete with spatial embedding of its organization, is an emergent property of a generative wiring equation that optimizes its connectivity by renegotiating its biological costs and topological values continuously over time. The rules that govern these iterative wiring properties are controlled by a set of tightly framed parameters, with subtle differences in these parameters steering network growth towards different neurodiverse outcomes. Regional expression of genes associated with the simulations converge on biological processes and cellular components predominantly involved in synaptic signaling, neuronal projection, catabolic intracellular processes and protein transport. Together, this provides a unifying computational framework for conceptualizing the mechanisms and diversity in neurodevelopment, capable of integrating different levels of analysis—from genes to cognition

Genetic mechanisms of critical illness in COVID-19.

Host-mediated lung inflammation is present1, and drives mortality2, in the critical illness caused by coronavirus disease 2019 (COVID-19). Host genetic variants associated with critical illness may identify mechanistic targets for therapeutic development3. Here we report the results of the GenOMICC (Genetics Of Mortality In Critical Care) genome-wide association study in 2,244 critically ill patients with COVID-19 from 208 UK intensive care units. We have identified and replicated the following new genome-wide significant associations: on chromosome 12q24.13 (rs10735079, P = 1.65 × 10-8) in a gene cluster that encodes antiviral restriction enzyme activators (OAS1, OAS2 and OAS3); on chromosome 19p13.2 (rs74956615, P = 2.3 × 10-8) near the gene that encodes tyrosine kinase 2 (TYK2); on chromosome 19p13.3 (rs2109069, P = 3.98 ×  10-12) within the gene that encodes dipeptidyl peptidase 9 (DPP9); and on chromosome 21q22.1 (rs2236757, P = 4.99 × 10-8) in the interferon receptor gene IFNAR2. We identified potential targets for repurposing of licensed medications: using Mendelian randomization, we found evidence that low expression of IFNAR2, or high expression of TYK2, are associated with life-threatening disease; and transcriptome-wide association in lung tissue revealed that high expression of the monocyte-macrophage chemotactic receptor CCR2 is associated with severe COVID-19. Our results identify robust genetic signals relating to key host antiviral defence mechanisms and mediators of inflammatory organ damage in COVID-19. Both mechanisms may be amenable to targeted treatment with existing drugs. However, large-scale randomized clinical trials will be essential before any change to clinical practice

Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination

A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain circumstances. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states -- ideally without error and with unit success probability. This is a generalised quantum measurement with six outcomes, where each outcome corresponds to excluding a pair of states. Our experimental realisation uses single photons, with information encoded in a four-dimensional state using optical path and polarisation degrees of freedom. The prepared state is incorrectly ruled out up to $3.3(2)\%$ of the time.Comment: 11 pages, 3 figure