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Logical Entropy: Introduction to Classical and Quantum Logical Information Theory

机译:逻辑熵:古典和量子逻辑信息理论简介

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摘要

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions (“dits”) of a partition (a pair of points distinguished by the partition). All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates (cohered together in the pure superposition state being measured) that are distinguished by the measurement (decohered in the post-measurement mixed state). Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states.
机译:逻辑信息理论是分区逻辑的定量版本,就像逻辑概率理论是子集的双布尔逻辑的定量版本。由此产生的信息概念是关于区别,差异和可区分性,并且使用分区的区分(“dits”)正式(由分区区分的一对点)。 Shannon信息理论的简单,关节,条件和相互熵的所有定义都是通过逻辑级别的相应定义的均匀转换来源的。本文的目的是给出与量子逻辑信息理论的直接泛化,其类似地侧重于观察到的观察到的特征酯对。,即可观察到的Qudits。量子逻辑熵和测量的基本定理建立了量子逻辑熵的增加,由于投影测量而导致的量子逻辑熵增加(在测量的纯叠加状态中缔合在一起)(拆卸在后测量混合状态)。逻辑熵的经典和量子版本都具有简单的解释,作为“双绘制”概率的区别。结论是量子逻辑熵是对衡量量子州的量子信息理论信息的简单而自然的概念。

著录项

  • 期刊名称 Entropy
  • 作者

    David Ellerman;

  • 作者单位
  • 年(卷),期 2018(20),9
  • 年度 2018
  • 页码 679
  • 总页数 22
  • 原文格式 PDF
  • 正文语种
  • 中图分类
  • 关键词

    机译:逻辑熵;分区逻辑;可观察到的QUDITS;
  • 入库时间 2022-08-21 12:20:29

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