Entanglement and thermodynamics in general probabilistic theories
Entanglement and thermodynamics in general probabilistic theories
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DOI：
10.1088/1367-2630/17/10/103027
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发表时间：
2015-10-14
影响因子：
3.3
通讯作者：
Scandolo, Carlo Maria
中科院分区：
文献类型：
--
作者：
Chiribella, Giulio;Scandolo, Carlo Maria
纠缠是量子力学最显著的特征之一，但它并不是特定的量子。更具体的量子力学是纠缠和热力学之间的联系，这导致了熵和纯态纠缠的测量之间的识别。在这里，我们寻找这种联系的根源，研究纠缠和热力学之间的关系，在一般概率理论的框架。我们首先解决的问题是，一个纠缠态是否可以通过局域操作和经典通信转换成另一个纠缠态。在两个操作要求下，我们证明了Lo-Popescu定理的一般版本，该定理是纯态纠缠理论的基础。然后，我们考虑一个资源理论的纯度，自由操作是随机可逆的转换，模拟的情况下，代理人有有限的控制一个封闭系统的动态。我们的关键结果是纠缠的资源理论和纯度的资源理论之间的二元性，有效的每一个物理理论，其中所有的过程产生于纯态和可逆的相互作用在基本水平。作为主要结果的应用，我们建立了熵与纯二体纠缠度量之间的一一对应关系。然后使用对应关系来定义一般概率框架中的纠缠度量。最后，我们展示了信息擦除任务和纠缠生成任务之间的对偶性，由此熵汇（可以吸收任意量信息的系统）的存在等价于纠缠源（可以提取任意量纠缠的相关系统）的存在。
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement. The correspondence is then used to define entanglement measures in the general probabilistic framework. Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).