Resource theories and their applications in quantum thermodynamics and nonlocality

Nelly Huei Ying Ng, Mischa P. Woods

Nicole Yunger Halpern

Carlo Sparaciari

Resource theories are a set of tools, coming from the field of quantum information theory, that find applications in the study of several physical scenarios. These theories describe the physical world from the perspective of an agent, who acts over a system to modify its quantum state, while having at disposal a limited set of operations. A noticeable example of a physical theory which has recently been described with these tools is quantum thermodynamics, consisting in the study of thermodynamic phenomena at the nano-scale. In the standard approach to resource theories, it is usually the case that the constraints over the set of available operations single out a unique resource. In this thesis, we extend the resource theoretic framework to include situations where multiple resources can be identified, and we apply our findings to the study of quantum thermodynamics, to gain a better understanding of quantities like work and heat in the microscopic regime. We introduce a mathematical framework to study resource theories with multiple resources, and we explore under which conditions these multi-resource theories are reversible. Furthermore, we investigate the interconversion of resources, i.e., in which situations it is possible to exchange between two different kinds of resources. We then apply this formalism to quantum thermodynamics, where the two resources under consideration are energy and entropy. This multi-resource theory allows us to explore thermodynamics when the system under examination is closed or coupled with a thermal environment with a finite size. In addition to our work on multi-resource theories, we study the states of equilibrium of closed systems, known as passive states, and analyse under which circumstances it is possible to extract energy from these states. We show that passivity is energetically unstable, and that, even for closed systems, the only stable states are those with a well-defined temperature.

Lídia del Rio, Lea Krämer, Renato Renner

How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.

Iman Marvian

Matteo Lostaglio

In these notes I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics covered include the `many second laws of thermodynamics', thermo-majorisation and symmetry constraints on the evolution of quantum coherence. Among the elementary applications, I explicitly work out the bounds on deterministic work extraction and formation, discuss the complete solution of the theory for a single qubit and present the irreversibility of coherence transfers. The aim is to facilitate the task of those researchers interested in engaging and contributing to this topic, also discussing the relation between the resource theory and complementary approaches.