Local unitary versus local Clifford equivalence of stabilizer states

We study the relation between local unitary (LU) equivalence and local Clifford (LC) equivalence of stabilizer states. We introduce a large subclass of stabilizer states, such that every two LU equivalent states in this class are necessarily LC equivalent. Together with earlier results, this shows that LC, LU and SLOCC equivalence are the same notions for this class of stabilizer states. Moreover, recognizing whether two given stabilizer states in the present subclass are locally equivalent only requires a polynomial number of operations in the number of qubits.Comment: 8 pages, replaced with published versio

ARGOS policy brief on semantic interoperability

Semantic interoperability requires the use of standards, not only for Electronic Health Record (EHR) data to be transferred and structurally mapped into a receiving repository, but also for the clinical content of the EHR to be interpreted in conformity with the original meanings intended by its authors. Accurate and complete clinical documentation, faithful to the patient’s situation, and interoperability between systems, require widespread and dependable access to published and maintained collections of coherent and quality-assured semantic resources, including models such as archetypes and templates that would (1) provide clinical context, (2) be mapped to interoperability standards for EHR data, (3) be linked to well specified, multi-lingual terminology value sets, and (4) be derived from high quality ontologies. Wide-scale engagement with professional bodies, globally, is needed to develop these clinical information standards

On the geometry of entangled states

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general very hard, we show that the following strongly related problem can be solved: find the Hilbert Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial transpose of the entangled state, and show how it is related to the distance of a state to the set of positive partially transposed states (PPT-states). We illustrate this by calculating the closest biseparable state to the W-state, and give a simple and very general proof for the fact that the set of W-type states is not of measure zero. Next we show that all surfaces with states whose partial transposes have constant minimal negative eigenvalue are similar to the boundary of PPT states. We illustrate this with some examples on bipartite qubit states, where contours of constant negativity are plotted on two-dimensional intersections of the complete state space.Comment: submitted to Journal of Modern Optic

The Size Distribution and Shape of Curd Granules in Traditional Swiss Hard and Semi-Hard Cheeses

Curd granule junction patterns in hard (Emmentaler, Gruyere, Sbrinz) and semi-hard cheeses (Appenzeller , Tilsiter, Raclette) were visualized on slices and examined using light microscopy and digital image analysis. Horizontal and vertical sections were cut in different zones of the loaves, in order to obtain information on the orientation of the flattened curd granules. The frequency histograms of the cross section areas could in most cases adequately be described as a log-normal distribution. The median values ranged from 0.97 to 1.15 mm2 and, from 1.31 to 1.68 mm2 for hard and semi-hard cheeses, respectively. An elliptical form factor was used as a measure of the deformation of the granules. The average ratio of the elliptical axes was in the range of 0 .41 to 0.56 in horizontal and 0.33 to 0.48 i n vertical sections. The difference between the form factors in the orthogonal sections was less pronounced in the Appenzeller and Tilsiter cheeses than in the other varieties. Significantly different junction patterns were observed in regions of the edges and sides of the original billets of curd . The micrographs reveal ed interesting features around the eyes and in the cheese rind. Semi-mechanized and traditionally manufactured Appenzeller and Tilsiter cheeses had different curd granule junction patterns, mainly because of different moulding and pressing arrangements

Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic

We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over the integers modulo d. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.Comment: 10 pages, RevTe