Chong Li, He-Shan Song, Ling Zhou
A new notation has been introduced for the quantum information theory. By this notation,some calculations became simple in quantum information theory such as quantum swapping, quantum teleportation.
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We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic quantum information theory. We then use this formulation to consider the transformation properties of qubits and density matrices under space-time and gauge transformations. Finally we use our results to understand the behaviour of entanglement between different partitions of quantum systems. Our approach not only clarifies the notation, but provides a more intui…
Visualizing Entanglement in multi-Qubit Systems
该研究提出用量子比特圆符号结合n维空间表示思路的维度圆符号法可视化多量子比特系综，证明可分性数学条件对应可视化态的对称性，为量子纠缠研究提供新视角，可作为直观认知与数学描述的桥梁。
Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education
本先导研究针对量子信息科学教育中数学门槛高的问题，对比纯狄拉克记号与结合圆记号可视化的教学方式，通过定性访谈与定量测试验证可视化对学生解题表现、认知负荷的影响，为后续大规模研究提供假设依据。
This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra formalism, and it turns out that one has an allover dualism of language: we can define everything for (compatible) observables, but also for (compatible) C*-subalgebras. The two approaches are unified in the formalism of quantum operations, and they are connected by a very satisfying inequality, generalizing the well known Holevo bound. Then we turn to communicatio…
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information transmission via quantum channels we give a new proof of the coding theorem, and prove the strong converse, even under the extended model of nonstationary channels. As a by-product we obtain a new proof of the famous Holevo bound. Then multi-user systems are investigated, and the capacity region for the quantum multiple access channel is determined. The last chapter c…
We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and operations with the help of Jamiolkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations we utilize a package for the Mathematica computing system implementing basic functions used in…
Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems. This may, however, no longer be true for three or more party quantum systems. In this paper, we propose an alternative definition of multipartite information taking into account the shared information between two and more parties. It is non-negative, observes monotonicity under partial trace as well as completely positive maps, and equals multip…
A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the $N$ agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement $σ_x \otimes σ_x$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the in…
These are the lecture notes of guest lectures for Artur Ekert's course Introduction to Quantum Information at the Mathematical Institute of Oxford University, Hilary Term 2023. Some basic familiarity with Dirac notation is assumed. For the readers of Quantum in Pictures (QiP) who have some basic quantum background, these notes also constitute the shortest path to an explanation of how what they learn in QIP relates to the traditional quantum formalism.
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding probabilities. In this work we keep the first group of postulates and characterize all alternatives to the second group that give rise to finite-dimensional sets of mixed states. We prove a correspondence between all these alternatives and a class of representations of the unitary group. Some features of these probabilistic theories are identical to quantum theory, but …
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax directly captures the structure of the entangled states used to represent computations, and show that the notion of information flow within the entangled states gives rise to rewriting strategies for proving the correctness of quantum programs.
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to the system, results in a change of degrees of freedom, uncovering the information hidden in non-local degrees of freedom. This information can be used, inter alia, to study the structure of entangled states, their classification and may be useful for construction of quantum algorithms.
Comment on "Multiparty quantum mutual information: An alternative definition"
本文反驳了Kumar关于量子对偶总关联可表示为特定量子相对熵的论断，指出该表示对$n\geq3$的广义GHZ态不成立。
Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
本文是一篇面向初学者的教程，仅用线性代数基础介绍量子信息中的 Haar 测度工具，涵盖矩算子、酉设计及其近似概念，并展示其在量子机器学习与经典阴影层析中的应用。
The paper "Physics without determinism: Alternative interpretations of classical physics" [Phys. Rev. A, 100:062107, Dec 2019] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity. We show that a change in the measurement unit does not preserve the information carried by a FIQ, and therefore that the definition provided in the paper is not complete.
Information Is Not Physical: Possibility Spaces, Erasure, and the Structure of Unrealized Alternatives
本文提出信息是物理可实现替代的结构，而非物理实体或数学抽象，通过反事实解读解决擦除耗热、量子叠加信息丰富性及黑洞信息损失等困惑。
We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case we find the threshold rate, the optimal error and strong converse exponents (at large deviations from the threshold) and the second order asymptotics (at small deviations from the threshold). We apply our results to find operational interpretations of various Renyi information measures. In case the alternative hypothesis is comprised of bipartite product distribu…
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