## Paolo Solinas

*Institure CNR-SPIN*

Paolo Solinas is a researcher at the SPIN Institute of the CNR in Genova (Italy). He did his PhD at the University of Genova (Italy) under the supervision of Prof. N. Zanghì and Prof. P. Zanardi. After a postdoc in Paris (France) at the LPTMC (Laboratory of Theoretical Physics of Condensed Matter) and at Aalto University in Helsinki (Finland), he returned to Genova with a researcher position. His research interests include different subjects related to the quantum technologies including geometric and topological quantum information, open quantum system and superconducting implementation of quantum devices.

**Introduction **

The concept of work and heat are two cornerstones of classical physics. Work allows us to answer to a fundamental and practical question: how much energy does a system need to perform a specific task?

In classical thermodynamics, under plausible hypothesis, work and heat are related by the first law of thermodynamics. The advantages and elegance of such quantities relies on the fact that they can be calculated neglecting the details of the system and the dynamics.

Surprisingly, the discussion on how to extend the concept of work to the quantum domain has not been faced until recently. Even then, the extension of the concept of work to the quantum domain has proved to be rather problematic.

That is because the quantum work cannot be associated to a standard Hermitian operator. Thus, it touches the deepest root of the foundation of quantum mechanics.

**Results **

Here, we approach the problem from an operational perspective and consider a setup in which the internal energy of a closed system is recorded by a quantum detector before and after the system is acted upon by an external drive.

We show how the resulting work statistics depends on the initial state of the detector as well as on the choice of the final measurement.

In particular, the presence of quantum coherences in the initial state of the system leads to a quasiprobability distribution of work and to the violation of the corresponding Leggett-Garg inequalities.

We consider two complementary measurement schemes, both of which show clear signatures of quantum interference and specifically discuss how to implement these schemes in the circuit QED architecture.

**Discussion**

From these results we conclude that the quantum work statistics cannot be uniquely determined and it depends on the kind of measurement used and perturbation induced in the measurement procedure.

Despite the fact that this can seem unsatisfactory, it highlights the very quantum nature of work and it opens the way to the exploitation the pure quantum effects to optimize the energy storing and manipulating in driven quantum systems.

Fundamental science for quantum technologies , Superconducting circuits