Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics
Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics
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DOI：
10.1103/physrevlett.115.210403
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发表时间：
2015-11-18
影响因子：
8.6
通讯作者：
Oppenheim, Jonathan
中科院分区：
文献类型：
--
作者：
Cwiklinski, Piotr;Studzinski, Michal;Oppenheim, Jonathan
热力学第二定律限制了一个系统可以进化到的状态。对于与热浴接触的系统，它可以与能量守恒定律结合起来，它说，一个系统只能在自由能下降的情况下进化成另一个系统。最近的研究表明，实际上存在着许多第二定律，只有对于大的宏观系统，它们才与普通的第二定律等价。这些附加的第二定律也适用于量子系统，事实上，在这个体系中通常更相关。它们限制了能级的概率如何演化。在这里，我们考虑额外的限制，如何在能级之间的相干性可以演变。一致性只能下降，我们提供了一组限制，限制了它们可以保持的程度。我们发现，相干能级必须衰减的速度，是适当地适应能级之间的过渡率。我们表明，在一个单一的量子比特的情况下，匹配的限制，在这种情况下，我们得到的状态到状态的转换的充分表征。对于更高的维度，我们推测存在更严格的约束。我们还介绍了一类新的cohesive操作，允许更大的操纵cohesive和研究其权力方面的一类操作称为热操作。
The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations.