Abstract
Recent work using tools from quantum information theory has shown that at the nanoscale where quantum effects become prevalent, there is not one thermodynamical second law but many. Derivations of these laws assume that an experimenter has very precise control of the system and heat bath. Here we show that these multitude of laws can be saturated using two very simple operations: changing the energy levels of the system and thermalizing over any two system energy levels. Using these two operations, one can distill the optimal amount of work from a system, as well as perform the reverse formation process. Even more surprisingly, using only these two operations and one ancilla qubit in a thermal state, one can transform any state into any other state allowable by the second laws. We thus have the remarkable result that the second laws hold for fine-grained manipulation of system and bath, but can be achieved using very coarse control. This brings the full array of thermal operations into a regime accessible by experiment, and establishes the physical relevance of these second laws.
Highlights
Thermodynamics and statistical physics are one of the most successful areas of physics, owing to their broad applicability
IV, we show how applying protocols consisting of these operations to a system and a single thermal qubit is sufficient for implementing any transformation to a block-diagonal state that is possible under thermal operations
A partial level thermalizations (PLTs) is defined as Definition 2 (Partial level thermalizations).—A partial level thermalization on an n-level system is parametrized by λ ∈ 1⁄20; 1 and a subset P ⊆ f1; ...; ng of the system’s eHnaeGmrgiivyletonlneaviaednlisaH.gWSon1⁄4ealdPsetnani1⁄4otet1eEρiit1⁄4jibiyP hijPnii1⁄4Ln1TcηPoijnðiλtiaÞh.citj with with associated a heat bath at inverse temperature β, the action of PLTPðλÞ on ρ is given by ρPL⟶ TP ðλÞρ0 ; ð5Þ
Summary
Thermodynamics and statistical physics are one of the most successful areas of physics, owing to their broad applicability. The set of states that it is possible to transition to from a given starting state and converge to the familiar second law in the thermodynamic limit [13] Such precise control will be impossible to implement as it could require accurately manipulating all of the 1020 molecules contained in a typical heat bath. Here we show that any state transformation permitted by the additional second laws can be achieved using three simple operations These operations, which we term crude operations, are experimentally feasible for small systems and do not require fine control of bath d.o.f. to implement, only weak coupling to the bath. As a by-product, our simple operations can be viewed analogously to a universal gate set in quantum computing: they provide building blocks for the construction of more elaborate protocols
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