# On the classification of two-qubit group orbits and the use of coarse-grained ‘shape’ as a superselection property

Thomas Hebdige1 and David Jennings1,2,3

1Controlled Quantum Dynamics Theory Group, Imperial College London, Prince Consort Road, London SW7 2BW, UK
2Department of Physics, University of Oxford, Oxford, OX1 3PU, UK
3School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK.

### Abstract

Recently a complete set of entropic conditions has been derived for the interconversion structure of states under quantum operations that respect a specified symmetry action, however the core structure of these conditions is still only partially understood. Here we develop a coarse-grained description with the aim of shedding light on both the structure and the complexity of this general problem. Specifically, we consider the degree to which one can associate a basic shape' property to a quantum state or channel that captures coarse-grained data either for state interconversion or for the use of a state within a simulation protocol. We provide a complete solution for the two-qubit case under the rotation group, give analysis for the more general case and discuss possible extensions of the approach.

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### Cited by

[1] Cristina Cirstoiu and David Jennings, "Global and local gauge symmetries beyond Lagrangian formulations", arXiv:1707.09826.

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