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Journal of Statistical Mechanics: theory and experiment

The internet-a vast network that enables simultaneous long-range classical communication-has had a revolutionary impact on our world. The vision of a quantum internet is to fundamentally enhance internet technology by enabling quantum communication between any two points on Earth. Such a quantum internet may operate in parallel to the internet that we have today and connect quantum processors in order to achieve capabilities that are provably impossible by using only classical means. Here, we propose stages of development toward a full-blown quantum internet and highlight experimental and theoretical progress needed to attain them.

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Quantum internet: A vision for the road ahead

Annalen der Physik

This review introduces a new development in theoretical quantum physics, the ``resource-theoretic'' point of view. The approach aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory. This development is an extension of the principles of thermodynamics to quantum problems; but there are resources that would never have been considered previously in thermodynamics, such as shared knowledge of a frame of reference. Many additional examples and new quantifications of resources are provided.

Quantum resource theories

Sadi Carnot's theorem regarding the maximum efficiency of heat engines is considered to be of fundamental importance in thermodynamics. This theorem famously states that the maximum efficiency depends only on the temperature of the heat baths used by the engine, but not on the specific structure of baths. Here, we show that when the heat baths are finite in size, and when the engine operates in the quantum nanoregime, a revision to this statement is required. We show that one may still achieve the Carnot efficiency, when certain conditions on the bath structure are satisfied; however if that is not the case, then the maximum achievable efficiency can reduce to a value which is strictly less than Carnot. We derive the maximum efficiency for the case when one of the baths is composed of qubits. Furthermore, we show that the maximum efficiency is determined by either the standard second law of thermodynamics, analogously to the macroscopic case, or by the non increase of the max relative entropy, which is a quantity previously associated with the single shot regime in many quantum protocols. This relative entropic quantity emerges as a consequence of additional constraints, called generalized free energies, that govern thermodynamical transitions in the nanoregime. Our findings imply that in order to maximize efficiency, further considerations in choosing bath Hamiltonians should be made, when explicitly constructing quantum heat engines in the future. This understanding of thermodynamics has implications for nanoscale engineering aiming to construct small thermal machines.

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The maximum efficiency of nano heat engines depends on more than temperature

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity, and asymmetry. Such frameworks are characterized by two main elements: a set of predefined (free) operations and states, that one assumes to be easily obtained at no cost. Given these ground rules, one can ask: what is achievable by using such free operations and states? This usually results in a set of state transition conditions, that tell us if a particular state $ \rho $ may evolve into another state $ \rho ' $ via the usage of free operations and states. We shall see in this chapter that thermal interactions can be modelled as a resource theory. The state transition conditions arising out of such a framework, are then referred to as “second laws”. We shall also see how such state transition conditions recover classical thermodynamics in the i.i.d. limit. Finally, we discuss how these laws are applied to study fundamental limitations to the performance of quantum heat engines.

Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity, and asymmetry. Such frameworks are characterized by two main elements: a set of predefined (free) operations and states, that one assumes to be easily obtained at no cost. Given these ground rules, one can ask: what is achievable by using such free operations and states? This usually results in a set of state transition conditions, that tell us if a particular state $ \rho $ may evolve into another state $ \rho' $ via the usage of free operations and states. We shall see in this chapter that thermal interactions can be modelled as a resource theory. The state transition conditions arising out of such a framework, are then referred to as "second laws". We shall also see how such state transition conditions recover classical thermodynamics in the i.i.d. limit. Finally, we discuss how these laws are applied to study fundamental limitations to the performance of quantum heat engines.

Resource theory of quantum thermodynamics: Thermal operations and Second Laws

The work performed on or extracted from a nonautonomous quantum system described by means of a two-point projective-measurement approach is a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum R\'enyi-$\ensuremath{\alpha}$ divergences, and by exploiting the convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics, a theory in which R\'enyi-$\ensuremath{\alpha}$ divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstructing the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource-theoretic settings.

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Quantum work statistics and resource theories: Bridging the gap through Rényi divergences.

/pdf/the-maximum-efficiency-of-nano-heat-engines-depends-on-more-3gqpbjyi6y.pdf

Nelly Huei Ying Ng

Papers

The maximum efficiency of nano heat engines depends on more than temperature

Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

Resource theory of quantum thermodynamics: Thermal operations and Second Laws

Quantum work statistics and resource theories: Bridging the gap through Rényi divergences.

The maximum efficiency of nano heat engines depends on more than temperature