Zhaoqi Wu, Lin Zhang, Jianhui Wang, Xianqing Li-Jost, Shao-Ming Fei
Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information.
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In this paper, we consider Wigner-Yanase-Dyson information as a measure of quantum uncertainty of a mixed state. We study some of the interesting properties of this generalized measure. The construction is reminiscent of the generalized entropies that have shown to be useful in many applications.
Tighter sum uncertainty relations via $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information
该研究利用$(α,β,γ)$WWYD斜信息为任意有限可观测量建立更紧的和不确定关系，并借助$(α,β,γ)$MWWYD斜信息给出量子信道与酉信道的更紧下界。
We introduce ($α,β,γ$) weighted Wigner-Yanase-Dyson (($α,β,γ$) WWYD) skew information and ($α,β,γ$) modified weighted Wigner-Yanase-Dyson (($α,β,γ$) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary $N$ mutually noncommutative observables based on ($α,β,γ$) WWYD skew information. A series of uncertainty inequalities are derived. We show by detailed example that our results cover and improve the previous ones based on the original Wigner-Yanase (WY) skew information. Finally, we establish new sum uncertainty relations in terms of the ($α,β,γ$) MWWYD skew informatio…
We present uncertainty relations based on Wigner--Yanase--Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. \mbox{It is} shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed examples are given for product, separable and entangled states.
In this paper, we give a Schrödinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schrödinger-type uncertainty relation by use of a two-parameter extended correlation measure. Moreover, we give the further generalization for Schrödinger-type uncertainty relation by metric adjusted correlation measure. These results generalize our previous result in [Phys. Rev. A, Vol.82(2010), 034101].
The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the decomposition of the variance, a stronger uncertainty relation was presented by Luo in [Phys. Rev. A 72, 042110 (2005)]. In this paper, by using Wigner-Yanase-Dyson information which is a generalization of the skew information, we propose a general uncertainty relation of mixed states.
Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
本文提出量子信道的 $(α,β,γ)$ MWWYD 偏斜信息新形式，利用算子范数不等式推导出任意 $N$ 个量子信道与酉信道更紧致的求和不确定性关系，并通过实例验证，其特例亦适用于 MWWYD 与 $(α,γ)$ MWWYD 偏斜信息。
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixure. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued.
In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained.
A connection of the Wigner-Yanase skew information and multiple quantum (MQ) NMR coherences is considered at different temperatures and evolution times of nuclear spins with dipole-dipole interactions in MQ NMR experiments in solids. It is shown that the Wigner-Yanase skew information at temperature $T$ is equal to the double second moment of the MQ NMR spectrum at the double temperature for any evolution times. A comparison of the many-spin entanglement obtained with the Wigner-Yanase information and the Fisher information is conducted.
Wigner-Yanase skew information-based uncertainty relations for quantum channels
本文针对两个量子信道，利用 Wigner-Yanase 斜信息建立乘积与求和形式的紧致不确定关系，并证明其优于已有结果。
We study sum uncertainty relations for arbitrary finite $N$ quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.
We shall give a new Schrödinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed state.
Generalized Wigner-Yanase Skew Information and the Affiliated Inequality
该研究提出一族包含Wigner-Yanase斜信息与量子Fisher信息为特例的广义斜信息，证明其凸性并简化Wigner-Yanase-Dyson猜想证明，还得到了量子比特系统斜信息不等式及不同维度下的上下界。
Measurement-induced nonlocality (MIN) was proposed for measure the maximum global effect caused by locally invariant measurements. Similarly, the Measurement-induced nonbilocal correlation is a generalization of MIN can be used to measure the maximal global influence caused by the local measurement in the bilocal scenario. In this paper, we propose a new nonbilocal correlation measure based on the Wigner-Yanase skew information. The relationship between the MIN based on Wigner-Yanase skew information and our measure is discussed. We present an analytical expression of our measure for pure inpu…
We give a trace inequality related to the uncertainty relation of generalized Wigner-Yanase-Dyson skew information which includes our result in JMAA, vol.365, pp.12-18, 2010.
Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and quantum uncertainty of quantum channels. The elegant properties of the total uncertainty of quantum channels are explored in detail. In addition, we present a trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity and establish the relationships between the total uncertainty and entropy exchange/coherent informatio…
We give a trace inequality related to the uncertainty relation of Wigner-Yanase-Dyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S. Luo for the quantum uncertainty quantity excluding the classical mixture.
We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty relations. Detailed examples are provided to illustrate the advantages of our uncertainty inequalities.
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic features of the state and the observable. In this paper, we mainly investigate the sum uncertainty relations for both quantum mechanical observables and quantum channels based on skew information. We establish a new uncertainty relation in terms of Wigner-Yanase skew information for $n$ observables, which is saturated (thus it holds as equality) for two incompatib…
A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light…
Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences (MQCs). Here we investigate the $α$-MQCs, a novel class of multiple quantum coherences which is based on $α$-relative purity, an information-theoretic quantifier analogous to quantum fidelity and closely related to Rényi relative entropy of order $α$. Our framework enables linking $α$-MQCs to Wigner-Yanase-Dyson skew information (WYDSI), an asymmetry monoto…
Several families of entanglement criteria for multipartite quantum systems based on generalized Wigner-Yanase skew information and variance
本文提出基于广义 Wigner-Yanase 斜信息与方差的几族纠缠判据，用于检测多体或高维量子系统中的纠缠，并证明两类判据具有互补性，组合后检测能力更强。
Quantifying nonclassical correlation via the generalized Wigner-Yanase skew information
本文引入广义 Wigner-Yanase 斜信息，基于局部可观测量分类提出量化二部量子态非经典关联的指标，证明其在纯态下退化为纠缠度量并推导了与 $I$-concurrence 的关系。
Multipartite entanglement detection via generalized Wigner-Yanase skew information
本文利用广义Wigner-Yanase斜信息构造两类不等式判据，实现对N体量子系统从2体到N体纠缠及不可分性的精细层级检测，并通过例子证明其能发现其他方法漏检的纠缠。
The first step of quantum measurement procedure is known as \emph{premeasurement}, during when correlation between measuring system and measurement apparatus is established. One compelling non-classical correlation is entanglement, a useful resource for various quantum information theoretic protocols. Quantifying the amount of entanglement in the premeasurement state, therefore, seeks importance from practical ground and this is the central issue of the present paper. Interestingly, for a two-label quantum system we obtain that the amount of entanglement, measured in term of \emph{negativity},…
Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information
本文提出了基于对称化ρ-绝对方差的不确定性关系，将其推广至量子信道，并利用Cauchy-Schwarz不等式建立了更紧的不确定性关系，通过示例验证了结果的紧致性。
We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in [Phys. Rev. Lett. \textbf{113}, 170401(2014)], can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.
The Wigner-Yanase skew information was proposed to quantify the information contained in quantum states with respect to a conserved additive quantity, and it was later extended to the Wigner-Yanase-Dyson skew informations. Recently, the Wigner-Yanase-Dyson skew informations have been recognized as valid resource measures for the resource theory of asymmetry, and their properties have been investigated from a resource-theoretic perspective. The Wigner-Yanse-Dyson skew informations have been further generalized to a class called metric-adjusted skew informations, and this general family of skew …
State-dependent and state-independent uncertainty relations for skew information and standard deviation
本文推导了包含不相容算子对易子的依赖于状态的不确定性等式，以及基于Wigner-Yanase偏斜信息的独立于状态的不确定性关系，将其推广至混合态和任意算子，并在量子比特中得到了更紧致的不等式与弱值测量方案。
A note on Wigner-Yanase skew information-based uncertainty of quantum channels
该研究针对含混合态的量子信道方差兼具经典与量子不确定性的问题，借助Wigner-Yanase斜信息探索方差分解方式，推广可观测量不确定性关系至信道，引入新量并推导了若干信道不确定性关系。
We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a family of coherence measures with respect to quantum channels is proposed. Furthermore, explicit analytical expressions of these coherence measures of qubit states are derived with respect to different quantum channels. Moreover, complementarity relations based on MGWYD skew information and MWGWYD skew information are also presented. Specifically, the conservatio…
Atomic non-classicality: A study of the anti-Jaynes-Cummings interaction
该研究以Wigner-Yanase斜信息为量化指标，分析反杰恩斯-卡明斯哈密顿量下二能级原子与单模压缩相干光耦合的原子非经典性动力学，发现参数变化下斜信息演化均呈混合态取值，与压缩效应一致。
Uncertainty Relation for the Wigner-Yanase Skew Information and Quantum Sobolev Inequalities
本文研究 Wigner-Yanase 斜信息等量子 Fisher 信息类似物的不确定性不等式，建立其与作者先前证明的量子 Sobolev 不等式的联系，并推导若干对易子不等式。
Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
研究噪声对横场Ising模型跨越量子临界点淬火的影响，发现无噪声时QFI和WYSI单调趋近绝热极限，而加入噪声后两者呈指数衰减，且最大斜坡时间与噪声方差线性标度。
Uncertainty principle plays a vital role in quantum physics. The Wigner-Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner-Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state…
Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.
We report a refinement of Robertson-Schroedinger uncertainty relation via Wigner-Yanase skew information. Besides the well known quantum uncertainty arising from the noncommutativity of observables, there is classical uncertainty arising from the mixedness of the states that is quantified by the difference between the variance and the skew information. Our refined uncertainty relation for canonical observables is saturated by all the Gaussian states, pure or mixed, and thus provides an alternative measure for the non-Gaussianity of quantum states. Generalizations to the case of metric adjusted…
In this paper we study the joint convexity/concavity of the trace functions \[ Ψ_{p,q,s}(A,B)=\text{Tr}(B^{\frac{q}{2}}K^*A^{p}KB^{\frac{q}{2}})^s,~~p,q,s\in \mathbb{R}, \] where $A$ and $B$ are positive definite matrices and $K$ is any fixed invertible matrix. We will give full range of $(p,q,s)\in\mathbb{R}^3$ for $Ψ_{p,q,s}$ to be jointly convex/concave for all $K$. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of $(α,z)$ for $α$-$z$ Rényi relative entropies to be monotone u…
Tighter sum uncertainty relations via metric-adjusted skew information
本文利用度量调整斜信息和三个范数不等式，提出有限可观测量与量子信道的更紧和不确定关系，并比较信道不确定性的两类下界。
The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fi…
Detecting $k$-nonseparability and $k$-partite Entanglement with Generalized Skew Information and Mutually Unbiased Measurements
本文提出基于广义Wigner-Yanase斜信息和互无偏测量的充分判据，用于检测多体系统中的$k$-不可分性与$k$体纠缠，并通过实例验证其检测能力，且可应用于量子网络深度识别。
Wigner-Yanase skew information, quantum entanglement and spin nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with single-ion anisotropies
本文利用Wigner-Yanase斜信息、二分纠缠熵和四极矩，研究了双二次自旋-1和自旋-2 XY链中自旋向列相间的量子相变，发现自旋-2系统存在拓扑相变和Ising普适类等丰富特性。
Quantifying nonclassical correlations relative to local channels
本文引入修正Wigner-Yanase-Dyson斜信息来量化量子态相对于局域信道的非经典关联，分析其基本性质并与现有度量比较，涵盖冯·诺依曼测量、酉信道和twirling信道。
Dynamic Evolution of Quantum Fisher and Skew Information under Decoherence in Three-Qubit X-States
该研究推导三量子比特X态的QFI与SQI解析表达式，分析三类退相干信道下的演化，并以GHZ态验证相位阻尼和相位翻转通常优于退极化。
The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as, the Wigner-Yanase-skew and quantum Fisher information are studied for a time-dependent coupled XY spin chain in presence of a time-dependent transverse magnetic field. Independent of the initial state of the system and while the relative entropy of coherence, $l_{1}$-norm of coherence, and quantum Fisher information are incapable, surprisingly, the dynamic Wigner-Yanase-skew information can truly spotlight the equilibrium critical point. We also observe that when the system is quenched to the critical point, these quan…
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the Hilbert-space setup the measure of uncertainty is given by the skew information of the second kind, while the uncertainty lower bound is given by the Wigner-Yanase skew information associated with the conjugate observable. Higher-order corrections to the uncertainty lower bound are determined by higher-order quantum skew moments; expressions for these moments are w…
We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for …
Enhanced quantum frequency estimation by nonlinear scrambling
本文研究在非线性量子电磁场中动态编码未知频率以增强频率估计，以能量成本为品质因数，证明高阶非线性过程通过量子置乱实现非线性增强，并利用Wigner-Yanase斜信息量化该效应，为优化非线性量子探针提供直接方法。
We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connec…
In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cramér-Rao inequality is expressed in terms of skew information. Since these two fundamental quantities are based on the concept of quantum uncertainty, we derive here their analytical formulas for arbitrary two qubit $X$-states using the same analytical procedures. A comparison of these two informational quantifiers for two quasi-Werner states composed of two bipartite superposed coherent s…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is essentially the normalized coherence of the entangled state in its Schmidt basis. Its value is 1 for maximally entangled states, and 0 for separable states, irrespective of the dimensionality of the Hilbert space. So a maximally entangled state is also the one which is maximally coherent in its Schmidt basis. Quantum entanglement and quantum coherence are thus intima…
Coherence-mixedness trade-offs
本研究基于l2范数相干性、条件冯·诺依曼熵和Wigner-Yanase偏斜信息，推导出量子态混合度对可达到相干性的基无关约束，推广了基相关关系，并量化了环境噪声对可提取相干性的限制。
We investigate the asymmetry properties of quantum states in relation to the Hamiltonian responsible for the magnetic dipolar interaction (MDI) dynamics, and we evaluate its relationship to entanglement production. We consider some classes of pure and mixed quantum states of two qubits evolved under MDI and, using the asymmetry measure defined via the Wigner-Yanase skew information, we describe the asymmetry dependence on the Hamiltonian parameters and initial conditions of the system. In addition, we define and calculate the dynamics of the asymmetry of local states, characterizing their temp…
We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states, i.e., the input states can be recovered from the output, if and only if the quantum Fisher information is preserved under the quantum channel. This class, for instance, includes Winger-Yanase-Dyson skew information. On the other hand, interestingly, the SLD quantum Fisher information, as the most popular example of quantum analog of Fisher information, does not satisfy this property. Our recoverability result is obtained by studying Riemannian monotone metrics on the q…
Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain less trivial and more robust physical constraints on quantum systems. In this sense, here we establish a geometric lower bound for the Wigner-Yanase skew information (WYSI), a well-known information theoretic quantity recently recognized as a proper quantum coherence measure. Starting from a mixed state evolving under unitary dynamics, while WYSI is a const…
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. However, for nanoscale systems deviations from standard thermodynamics arise due to their interactions with the environment. Here we include such interactions and, using quantum estimation theory, derive a generalised thermodynamic uncertainty relation valid for classical and quantum systems at all coupling strengths. We show that the non-commutativity between the system's state and its effective energy operator gives rise to quantum fluctuations that increase…
Conditional quantum thermometry -- enhancing precision by measuring less
本文提出以测量装置指针态为条件的广义热态，证明其在量子测温中优于吉布斯态，并从资源理论角度阐明精度提升源于Wigner-Yanase-Dyson斜信息所量化的非对称性。
Relations between different definitions of the quantum Wasserstein distance
本文研究了量子Wasserstein距离在qubit系统中单个算符出现在成本函数时不同定义之间的关系，发现自距离等于Wigner-Yanase斜信息。
Fisher discord as a quantifier of quantum complexity
本文借鉴量子失协思想，通过量子Fisher信息与Wigner-Yanase斜信息之差定义Fisher失协，作为量子态复杂度量化指标，并证明平衡态与纯态复杂度为零。
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