Entropic uncertainty relations in a class of generalized probabilistic theories
Entropic uncertainty relations in a class of generalized probabilistic theories
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DOI：
10.1088/1751-8121/ac0c5c
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发表时间：
2021-08-06
影响因子：
2.1
通讯作者：
Miyadera，Takayuki
中科院分区：
文献类型：
--
作者：
Takakura，Ryo;Miyadera，Takayuki
熵测不准关系在量子理论的基础和应用中起着重要的作用。虽然它们在量子理论中得到了很好的研究，但对广义概率理论（GPTs）中的熵不确定性知之甚少。目前的研究探讨了两种类型的熵不确定性关系，准备和测量不确定性关系，在一类GPT可以被认为是量子理论的推广。不仅提供了一种获得熵制备不确定度关系的方法，而且还提供了一种类似于布塞米等人（2014 Phys. Rev. Lett. 112 050401）在这些理论中得到了证明。这些结果表明，不确定关系中的熵结构并不局限于量子理论，而是普遍存在的。具体计算我们的关系在GPT称为正多边形理论也证明了。
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.