Pivoting makes the ZX-calculus complete for real stabilizers

We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.Comment: In Proceedings QPL 2013, arXiv:1412.791

Verifying the Steane code with Quantomatic

In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this represents the largest and most complicated verification task yet carried out using Quantomatic.Comment: In Proceedings QPL 2013, arXiv:1412.791

Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models

In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are inter-convertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete "operational" approach, in which the states and measurement outcomes associated with a physical system are represented in terms of what we here call a "convex operational model": a certain dual pair of ordered linear spaces -- generally, {\em not} isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term {\em weakly self-dual}, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol --- hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a {\em symmetric} bipartite state, the associated conditioning map of which is an isomorphism

Understanding and responding when things go wrong: key principles for primary care educators

Learning from events with unwanted outcomes is an important part of workplace based education and providing evidence for medical appraisal and revalidation. It has been suggested that adopting a ‘systems approach’ could enhance learning and effective change. We believe the following key principles should be understood by all healthcare staff, especially those with a role in developing and delivering educational content for safety and improvement in primary care. When things go wrong, professional accountability involves accepting there has been a problem, apologising if necessary and committing to learn and change. This is easier in a ‘Just Culture’ where wilful disregard of safe practice is not tolerated but where decisions commensurate with training and experience do not result in blame and punishment. People usually attempt to achieve successful outcomes, but when things go wrong the contribution of hindsight and attribution bias as well as a lack of understanding of conditions and available information (local rationality) can lead to inappropriately blame ‘human error’. System complexity makes reduction into component parts difficult; thus attempting to ‘find-and-fix’ malfunctioning components may not always be a valid approach. Finally, performance variability by staff is often needed to meet demands or cope with resource constraints. We believe understanding these core principles is a necessary precursor to adopting a ‘systems approach’ that can increase learning and reduce the damaging effects on morale when ‘human error’ is blamed. This may result in ‘human error’ becoming the starting point of an investigation and not the endpoint

Strong Complementarity and Non-locality in Categorical Quantum Mechanics

Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity. Since our main results are expressed in the (diagrammatic) language of dagger-compact categories, they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory. The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.Comment: 15 pages (incl. 5 appendix). To appear: LiCS 201

Understanding patient safety performance and educational needs using the ‘Safety-II’ approach for complex systems

Participation in projects to improve patient safety is a key component of general practice (GP) specialty training, appraisal and revalidation. Patient safety training priorities for GPs at all career stages are described in the Royal College of General Practitioners’ curriculum. Current methods that are taught and employed to improve safety often use a ‘find-and-fix’ approach to identify components of a system (including humans) where performance could be improved. However, the complex interactions and inter-dependence between components in healthcare systems mean that cause and effect are not always linked in a predictable manner. The Safety-II approach has been proposed as a new way to understand how safety is achieved in complex systems that may improve quality and safety initiatives and enhance GP and trainee curriculum coverage. Safety-II aims to maximise the number of events with a successful outcome by exploring everyday work. Work-as-done often differs from work-as-imagined in protocols and guidelines and various ways to achieve success, dependent on work conditions, may be possible. Traditional approaches to improve the quality and safety of care often aim to constrain variability but understanding and managing variability may be a more beneficial approach. The application of a Safety-II approach to incident investigation, quality improvement projects, prospective analysis of risk in systems and performance indicators may offer improved insight into system performance leading to more effective change. The way forward may be to combine the Safety-II approach with ‘traditional’ methods to enhance patient safety training, outcomes and curriculum coverage

The adaptation of cognitive behavioural therapy for adult Maori clients with depression: A pilot study

A semistructured cognitive behavioural therapy (CBT) programme for depression was adapted for use with Maori adult clients with depression. Adaptations were developed in consultation with an advisory group consisting of Maori clinical psychologists and kaumatua with experience working in mental health services. The programme was piloted with 2 participants who were clients of a Maori mental health service. The programme builds on a more traditional CBT treatment programme by integrating concepts such as whakatauki, whanaungatanga, whanau involvement, and whakapapa into the therapeutic context. Despite limitations the results demonstrate considerable promise. Depressive symptoms increased substantially in both cases and both clients reflected positively on the adaptations incorporated into therapy