Beyond Euroscepticism: radical left and right ‘visions of Europe’ across party and protest arenas

This article makes a case for reassessing what counts as pro- or anti-European identity. Over the past decade, the rise of radical right mobilisations has prompted many progressive social movement organisations and parties within the EU to anchor their activism in a defence of ‘Europe’ and in resistance to nationalist retrenchment - even while maintaining strong critiques of specific EU policies. At the same time, actors on the radical right also and increasingly claim a European identi...

Continuity of Entropies via Integral Representations

We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity relation for the quantum relative entropy with respect to the first argument. Using it, we obtain a number of results: 1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, ...

Tight relations and equivalences between smooth relative entropies

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative entropy and the smoothed max-relative entropy, which together govern many operational settings. We first strengthen this connection into a type of equivalence: we show that the hypothesis testing relative entropy is equivalent to a variant of the smooth max-...

L'iscrizione medievale sul sarcofago Brenta-Torno