Universal Uncertainty Principle, Simultaneous Measurability, and Weak Values

Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.

平行与反平行自旋中的量子不相容性

Quantum Incompatibility in Parallel vs Antiparallel Spins

该研究探讨了平行与反平行自旋配置中量子不相容性的联合测量问题，揭示了反平行配置在预测自旋分量方面的独特优势，并探讨了其在加密协议和实验实现中的应用。

最不相容测量与平方和优化

Most incompatible measurements and sum-of-squares optimisation

通过平方和优化框架构造通用父测量，证明反交换可观测量集产生最不相容的二值测量，并改进高维量子导引的认证。

Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families

Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource requirements both by co-processing with a classical processor and by structuring computation into many subproblems. Each quantum subproblem involves a separate state preparation terminated by the measurement of one Pauli string. However, the number of such Pauli strings scales as $N^4$ for typical problems of interest--a daunting growth rate that poses a serious li…

非厄米 Jaynes-Cummings 模型中的通用量子 Fisher 信息以及 Landau 类与拓扑类相变的同时发生

Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models

该研究分析两类非厄米 Jaynes-Cummings 模型，证明例外点相变处的量子 Fisher 信息具有跨参数、能级和相的超普适性，并揭示 Landau 类与拓扑类相变可同时发生。

Heisenberg's original derivation of the uncertainty principle and its universally valid reformulations

Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the constraint that the product of their mean errors should be no less than a limit set by Planck's constant. However, Heisenberg with the subsequent completion by Kennard has long been credited only with a constraint for state preparation represented by the product of the standard deviations. Here, we show that Heisenberg actually proved the constraint for the ac…

量子态与SPAM噪声同时层析的通用框架

Universal framework for simultaneous tomography of quantum states and SPAM noise

提出一种同时层析量子态与测量噪声的通用去噪算法，基于酉操作诱导的线性算符空间性质，在单一规范自由度下表征SPAM误差，并利用先验知识打破简并性及减少测量次数。

Linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state

So-called quantum limits and their achievement are important themes in physics. Heisenberg's uncertainty relations are the most famous of them but are not universally valid and violated in general. In recent years, the reformulation of uncertainty relations is actively studied, and several universally valid uncertainty relations are derived. On the other hand, several measuring models, in particular, spin-1/2 measurements, are constructed and quantitatively examined. However, there are not so many studies on simultaneous measurements of position and momentum despite their importance. Here we s…

Contextual, Optimal and Universal Realization of the Quantum Cloning Machine and of the NOT gate

A simultaneous realization of the Universal Optimal Quantum Cloning Machine (UOQCM) and of the Universal-NOT gate by a quantum injected optical parametric amplification (QIOPA), is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.

Electromagnetism in terms of quantum measurements

We consider the question whether electromagnetism can be derived from quantum physics of measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way we justify the use of von Neumann-type measurement models for physical processes. We apply operational quantum measurement theory to gain insight in fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator…

基于多体Bell场景的通用测量型量子计算的经典模拟

Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios

本研究提出基于多体Bell场景非信号多胞体的经典模拟算法，可模拟通用测量型量子计算，明确量子加速的必要条件，拓展了可高效模拟的量子态范围。

Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, t…

非对易可观测量的同时测量：正变换与仪器李群

Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups

本研究提出无需量子态的仪器流形方案，通过仪器李群描述非对易可观测量的微分弱同时测量，关联随机主方程，引入通用仪器李群，分析主仪器特性并以三类基本测量为例验证其趋近强测量的规律。

Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under attack of a malignant third party. These codes are robust to different kinds of channel uncertainty. To construct such universal codes, we invoke and generalize properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to the capacity of compound quantum channels for simultaneously transmitting and generating entangleme…

Uncertainty relations: An operational approach to the error-disturbance tradeoff

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the act…