Trades in complex Hadamard matrices

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order $n$ all trades contain at least $n$ entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar $c \neq 1$ to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order $n$ and show that they all contain at least $n$ entries. We conjecture that all trades in complex Hadamard matrices contain at least $n$ entries.Comment: 9 pages, no figure

Exotic complex Hadamard matrices, and their equivalence

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequence

Dissociable contributions of mediodorsal and anterior thalamic nuclei in visual attentional performance: a comparison using nicotinic and muscarinic cholinergic receptor antagonists

Background: Thalamic subregions mediate various cognitive functions, including attention, inhibitory response control and decision making. Such neuronal activity is modulated by cholinergic thalamic afferents and deterioration of such modulatory signaling has been theorised to contribute to cognitive decline in neurodegenerative disorders. However, the thalamic subnuclei and cholinergic receptors involved in cognitive functioning remain largely unknown. Aims: We investigated whether muscarinic or nicotinic receptors in the mediodorsal thalamus and anterior thalamus contribute to rats’ performance in the five-choice serial reaction time task, which measures sustained visual attention and impulsive action. Methods: Male Long-Evans rats were trained in the five-choice serial reaction time task then surgically implanted with guide cannulae targeting either the mediodorsal thalamus or anterior thalamus. Reversible inactivation of either the mediodorsal thalamus or anterior thalamus were achieved with infusions of the γ-aminobutyric acid-ergic agonists muscimol and baclofen prior to behavioural assessment. To investigate cholinergic mechanisms, we also assessed the behavioural effects of locally administered nicotinic (mecamylamine) and muscarinic (scopolamine) receptor antagonists. Results: Reversible inactivation of the mediodorsal thalamus severely impaired discriminative accuracy and response speed and increased omissions. Inactivation of the anterior thalamus produced less profound effects, with impaired accuracy at the highest dose. In contrast, blocking cholinergic transmission in these regions did not significantly affect five-choice serial reaction time task performance. Conclusions/interpretations: These findings show the mediodorsal thalamus plays a key role in visuospatial attentional performance that is independent of local cholinergic neurotransmission

A Birkhoff connection between quantum circuits and linear classical reversible circuits

Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers

Pressure control of nonferroelastic ferroelectric domains in ErMnO3

Mechanical pressure controls the structural, electric, and magnetic order in solid-state systems, allowing tailoring of their physical properties. A well-established example is ferroelastic ferroelectrics, where the coupling between pressure and the primary symmetry-breaking order parameter enables hysteretic switching of the strain state and ferroelectric domain engineering. Here, we study the pressure-driven response in a nonferroelastic ferroelectric, ErMnO3, where the classical stress–strain coupling is absent and the domain formation is governed by creation–annihilation processes of topological defects. By annealing ErMnO3 polycrystals under variable pressures in the MPa regime, we transform nonferroelastic vortex-like domains into stripe-like domains. The width of the stripe-like domains is determined by the applied pressure as we confirm by three-dimensional phase field simulations, showing that pressure leads to oriented layer-like periodic domains. Our work demonstrates the possibility to utilize mechanical pressure for domain engineering in nonferroelastic ferroelectrics, providing a lever to control their dielectric and piezoelectric responses

Two remarks on generalized entropy power inequalities

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on

State tomography for two qubits using reduced densities

The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the number of interactions to be used. The algebraic method applied in the paper leads to an extension of the concept of mutually unbiased measurements.Comment: 8 pages LATE

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

The Limited Role of Mutually Unbiased Product Bases in Dimension Six

We show that a complete set of seven mutually unbiased bases in dimension six, if it exists, cannot contain more than one product basis.Comment: 8 pages, identical to published versio

Recommendations for collaborative paediatric research including biobanking in Europe: a Single Hub and Access point for paediatric Rheumatology in Europe (SHARE) initiative

Innovative research in childhood rheumatic diseases mandates international collaborations. However, researchers struggle with significant regulatory heterogeneity; an enabling European Union (EU)-wide framework is missing. The aims of the study were to systematically review the evidence for best practice and to establish recommendations for collaborative research. The Paediatric Rheumatology European Single Hub and Access point for paediatric Rheumatology in Europe (SHARE) project enabled a scoping review and expert discussion, which then informed the systematic literature review. Published evidence was synthesised; recommendations were drafted. An iterative review process and consultations with Ethics Committees and European experts for ethical and legal aspects of paediatric research refined the recommendations. SHARE experts and patient representatives vetted the proposed recommendations at a consensus meeting using Nominal Group Technique. Agreement of 80% was mandatory for inclusion. The systematic literature review returned 1319 records. A total of 223 full-text publications plus 22 international normative documents were reviewed; 85 publications and 16 normative documents were included. A total of 21 recommendations were established including general principles (1-3), ethics (4-7), paediatric principles (8 and 9), consent to paediatric research (10-14), paediatric databank and biobank (15 and 16), sharing of data and samples (17-19), and commercialisation and third parties (20 and 21). The refined recommendations resulted in an agreement of >80% for all recommendations. The SHARE initiative established the first recommendations for Paediatric Rheumatology collaborative research across borders in Europe. These provide strong support for an urgently needed European framework and evidence-based guidance for its implementation. Such changes will promote research in children with rheumatic diseases