Fundamental Limits on Anomalous Energy Flows in Correlated Quantum Systems.

In classical thermodynamics energy always flows from the hotter system to the colder one. However, if these systems are initially correlated, the energy flow can reverse, making the cold system colder and the hot system hotter. This intriguing phenomenon is called "anomalous energy flow" and shows the importance of initial correlations in determining physical properties of thermodynamic systems. Here we investigate the fundamental limits of this effect. Specifically, we find the optimal amount of energy that can be transferred between quantum systems under closed and reversible dynamics, which then allows us to characterize the anomalous energy flow. We then explore a more general scenario where the energy flow is mediated by an ancillary quantum system that acts as a catalyst. We show that this approach allows for exploiting previously inaccessible types of correlations, ultimately resulting in an energy transfer that surpasses our fundamental bound. To demonstrate these findings, we use a well-studied quantum optics setup involving two atoms coupled to an optical cavity.

Operational Definition of the Temperature of a Quantum State.

Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this Letter, we propose such a notion of temperature considering an operational task, inspired by the zeroth law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single- and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis," where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures. We demonstrate our findings using a two-level atom coupled to a single mode of the electromagnetic field.

Catalytic Quantum Teleportation.

In this work, we address fundamental limitations of quantum teleportation-the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e., without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application, e.g., in quantum thermodynamics.