Quantum Roundabout 2018 was the fourth iteration of a series of dedicated conferences looking at foundational mathematical topics within quantum physics.

The etymology of the conference stems from the so called “Magic Roundabout” on the outskirts of Swindon. This roundabout boasts five mini-roundabouts arranged around a sixth central anticlockwise roundabout. It was decided that such a strange junction could only be quantum in nature, hence the conception of Quantum Roundabout. The junction has since been named fourth scariest in Britain by a recent poll .

Held at the University of Nottingham every two years, Quantum Roundabout brings together early-career researchers from around the world to collaborate and engage in scientific discussion. The organisation of this conference is a rite of passage for all PhD students under the supervision of Professor Gerardo Adesso, who has overseen the organisation of all four iterations of the conference. Since its conception, attendance to Quantum Roundabout has grown significantly, with the most recent edition boasting over seventy attendees.

A specific motivation behind Quantum Roundabout is to provide a platform for early-career researchers to communicate their research and engage in scientific discussion, with a focus on new and emerging topics within quantum theory.

Each of the three days of the conference focused on a different theme with a morning and afternoon tutorial lead by an expert in the field. This year’s Quantum Roundabout covered the following areas of interest:

**Foundations of quantum thermodynamics.**Prof. Jonathan Oppenheim (UCL) delivered tutorials exploring the ultimate limitations for thermodynamic physical processes as formalised within the mathematical formalism of quantum resource theories.**Mathematical frontiers in quantum information.**Nilanjana Datta (University of Cambridge) drew our attention to the structure of Shannon theory and her recent contributions to majorization theory.**Resources for quantum technologies.**Prof. Matteo Paris (University of Milan) focused on the mathematical and statistical tools underpinning the implementation of quantum estimation theory and its range of applications.

Each of the tutorials underpinned the theme of the day, around which participants gave talks based on their current research.

A key goal of the Quantum Roundabout conference is to *highlight and promote the role of mathematics in the approach to quantum theory in both its fundamental and applied aspects. *

Indeed, mathematics is not just a tool when tackling a physical problem; sometimes it is the motivation behind the research, other times a mathematical theorem could be the ultimate result and, most of the time, the mathematical rigour becomes crucial in the understanding of physical concepts. This has been true in the past and still is today.

Recently, for example, the mathematical structure of *resource theories*, which has its roots in convex geometry, has found application in the burgeoning field of *quantum thermodynamics*. The classification of equilibrium states as free states and the energy preserving operations as free operations gives the laws of thermodynamics a mathematical foundation.

*Information theory*, originated by Shannon’s pioneering work, has provided versatile foundations for a variety of fields, which have attracted an increasing interest in recent years thanks to their potential for technological breakthroughs.

One of the most promising such technologies is* quantum metrology,* which studies the exploitation of quantum mechanical effects to develop measurement techniques that are higher in sensitivity or resolution than possible using classical systems alone.

As expressed by participants and the invited speakers, Quantum Roundabout 2018 delivered an effective platform for dedicated scientific discussion on emerging topics within the field. This atmosphere of discussion has since led to several collaborations between early-career researchers at international institutions. It is hoped that the continued success of Quantum Roundabout will help fuel future directions in the field of quantum theory and cement the University of Nottingham as a centre for quantum research.

This conference would not have been possible without the financial help of the IMA in addition to our other sponsors (LMS, JPhys.A, IAMP, Uni of Nottingham, IOP, Xanadu and FQXI). The organisers also wish to thank Prof. Gerardo Adesso, Dr Ludovico Lami, Dr Paul Knott and Katie Gill for their advice and support. Benjamin Morris would also like to thank his fellow organisers, Giorgio Nocerino, Buqing Xu and Carmine Napoli for making this year’s Quantum Roundabout a success.

*Written by Benjamin Morris*