This festive image has been taken from: Entanglement formation under random interactions by Christoph Wick *et al *from the Faculty of Physics and Astronomy, University of Würzburg and Quantum Universe Center at the Korea Institute for Advanced Study (KIAS).

In this work the authors studied the temporal evolution of the entanglement between two qubits evolving by random interactions.

The image shows an over-simplified cartoon of trajectories on the SU(4) group manifold, visualizing the two types of randomness; quenched and temporal, considered by the authors in this paper. The north pole (red arrow) stands for the identical transformation.

Our second image was found in the paper: Analytic vortex solutions on compact hyperbolic surfaces, by Rafael Maldonado and Nicholas Manton from The Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

Here, the authors show how to construct abelian Higgs vortices on compact hyperbolic surfaces that can be represented by tessellations of the hyperbolic plane by regular polygons. The image shows contour plots of |*ᶲ|*^{2} for a vortex at the centre of the fundamental octagon (left) and at a vertex (right).

This final image has been adapted from figure 2 in Mark Howard’s paper Classical codes in quantum state space. The authors have identified a construction relating the Hamming distance between *q*-ary strings to the Hilbert–Schmidt distance between certain Hermitian operators and the Fubini–Study distance between certain states.

This work is licensed under a Creative Commons Attribution 3.0 Unported License. Thumbnail image and figure 1 adapted from Christoph Wick *et al* 2016 *J. Phys. A: Math. Theor.* **49** 025303, figure 2 Rafael Maldonado and Nicholas S Manton 2015 *J. Phys. A: Math. Theor.* **48** 245403, figure 3 Mark Howard 2015 *J. Phys. A: Math. Theor.* **48** 495303 . Copyright IOP Publishing 2015.

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Categories: Journal of Physics A: Mathematical and Theoretical

Tags: Christmas, Image of the week, Mathematical physics, Quantum Entanglement, quantum physics, Statistical physics