University of Toronto（多伦多大学）；National Research Council of Canada（加拿大国家研究委员会）；The University of Hong Kong（香港大学）
Rui Jie Tang, Jeremy Guenza Marcus, Noah Lupu-Gladstein, Arthur O. T. Pang, C. Pria Dobney, Giulio Chiribella, Aephraim M. Steinberg, Y. Batuhan Yilmaz
We show that the quantum Fisher information about any phase parameter encoded in a family of pure quantum states can be faithfully compressed into a single qubit, accompanied by a logarithmic amount of classical bits. When the phase is encoded into many identical copies of a qubit state on the equator of the Bloch sphere, we show that the compression can be implemented sequentially, by iteratively compressing pairs of qubits into a single qubit. We experimentally demonstrate this building block in a photonic setup, developing two alternative compression strategies, based on Type-I fusion gate and a postselected implementation of the CNOT gate.
Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the principle of minimum Fisher information, we can derive the time-dependent Schrödinger equation step by step.
We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be directly obtained from the underlying dynamics. Examples are then provided to demonstrate the usefulness of the maximal quantum Fisher information matrix by deriving various tradeoff relations in multi-parameter quantum estimation and obtaining the bounds for the scalings of the precision limit.
In this paper, the dynamics of quantum Fisher information of a qubit interacting with a squeezed thermal environment are studied. The optimal initial state of the qubit, the temperature of the environment, and the interaction time, which maximize quantum Fisher information are obtained. Based on the ohmicity of the environment, we compare the dynamics of quantum Fisher information in ohmic, sub-ohmic, and super-ohmic regimes of the environment. Moreover, it is shown that the precise estimation of parameters is robust against squeezing.
Quantum Fisher information is a key concept in the field of quantum metrology, which aims to enhance the parameter accuracy by using quantum resources. In this paper, utilizing a representation of quantum Fisher information for a general unitary parametrization process, we study unitary parametrization processes governed by su(2) dynamics. We obtain the analytical expression for the Hermitian operator of the parametrization and the maximal quantum Fisher information. We find that the maximal quantum Fisher information over the parameter space consists of two parts, one is quadratic in the time…
We show that contrary to the claim in Sci. Rep. 7, 15492 (2017), the quantum Fisher information itself is not a valid coherence measure based on the resource theory of coherence because it can increase via an incoherent operation.
The dynamics of a charged two-qubit system prepared initially in a maximum entangled state is discussed, where each qubit interacts independently with a dephasing channel. The Fisher information is used to estimate the channel and the energy parameters. Moreover, the contribution from different parts of Fisher information is discussed. We show that, the degree of estimation of any parameter depends on the initial value of this parameter. It turns out that the upper bounds of Fisher information with respect to the dephasing parameter increase and that corresponding to coupling parameter decreas…
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(ΔA)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans. Inf. Theory 55, 439 (2009)]. We present an upper bound on this quantity that is proportional to the linear entropy. As expected, our relation shows that for states that are close to being pure, the quantum Fisher information over four is close to the variance. We also obtain the variance and the quantum F…
In this work we will study the Local quantum Fisher information and the local quantum uncertainty in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii Moriya (DM) interaction in z direction. Here we show that the DM interaction and spin interactions along the x, y, and z axis can increase and maintain local quantum Fisher information and local quantum uncertainty. It is also shown that because of thermal fluctuations local quantum Fisher information and local quantum uncertainty are decreased by increasing temperature. They are equal to one at very low temperature and starts to dec…
In the adiabatic perturbation theory, Berry curvature is related to the generalized force, and the quantum metric tensor is linked with energy fluctuation. While the former is tested with numerous numerical results and experimental realizations, the latter is less considered. Quantum Fisher information, key to quantum precision measurement, is four times quantum metric tensor. It is difficult to relate the quantum Fisher information with some physical observable. One interesting candidate is square of the symmetric logarithmic derivative, which is usually tough to obtain both theoretically and…
Fisher information and spin squeezing in the Lipkin-Meshkov-Glick Model
费舍尔信息，位于参数估计理论的核心，最近被发现与多体纠缠有密切的关系（Pezzé和Smerzi，Phys. Rev. Lett. 102，100401）。利用Fisher信息对Lipkin-Meskhov-Glick模型的基态行为进行了区分和表征，发现在对称相和破缺相之间存在一个二阶量子相变.我们发现，系统的参数灵敏度在破碎阶段达到海森堡极限，而在对称阶段，它只是在散粒噪声极限附近。基于参数估计的Fisher信息为我们提供了一种研究量子相变的方法。
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discor…
In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein-Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n=0,1,2 are calculated. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated.
A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of identically prepared quantum states that are Fisher symmetric for all pure states. Such measurements are optimal in achieving the minimal statistical error without adaptive measurements. We then determine all collective measurements on a pair that are Fisher symmetric for the completely mixed state and for all pure states simultaneously. For a qubit, these measurem…
We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation …
The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes. Here we show that by slightly modifying the definition of the Bures metric, the quantum information will be fully equivalent to the Bures metric without exception.
Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair ofspin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local …
We provide an experimentally measurable local gauge $U(1)$ invariant Fubini-Study (FS) metric for mixed states. Like the FS metric for pure states, it also captures only the quantum part of the uncertainty in the evolution Hamiltonian. We show that this satisfies the quantum Cramer-Rao bound and thus arrive at a more general and measurable bound. Upon imposing the monotonicity condition, it reduces to the square-root derivative quantum Fisher Information. We show that on the Fisher information metric space dynamical phase is zero. A relation between square root derivative and logarithmic deriv…
We explore quantum phase transitions in the spin-1/2 $XX$ chain with three-spin interaction in terms of local quantum Fisher information and one-way quantum deficit, together with the demonstration of quantum fluctuations. Analytical results are derived and analyzed in detail.
We study the changes in quantum Fisher information (QFI) values for one quantum system consisting of a superposition of W and GHZ states. In a recent work [6], QFI values of this mentioned system studied. In this work, we extend this problem for the changes of QFI values in some noisy channels. We show the change in QFI depending on noise parameters. We report interesting results for different type of decoherence channels.
Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example.
The standard quantum coherence theory is defined with respect to an orthonormal basis of a Hilbert space. Recently, Bischof, Kampermann and Bru% ß generalized the notion of coherence into the case of general measurements, and also, they established a rigorous resource theory of coherence with respect to general measurements. In this paper, we propose such a coherence measure with respect to general measurements via quantum Fisher information, and provide an application of this measure.
We derive criterion in the form of inequality based on quantum Fisher information and quantum variance to detect multipartite entanglement. It can be regarded as complementary of the well-established PPT criterion in the sense that it can also detect bound entangled states. The inequality is motivated by Y.Akbari-Kourbolagh $et\ al.$[Phys. Rev A. 99, 012304 (2019)] which introduced a multipartite entanglement criterion based on quantum Fisher information. Our criterion is experimentally measurable for detecting any $N$-qudit pure state mixed with white noisy. We take several examples to illust…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the probability distribution of the states contributing to the decomposition, and ii. quantum part given by the average quantum Fisher information of the states in this decomposition. Next we use a non-Hermitian extension of symmetric logarithmic derivative in order to obtain another upper bound on quantum Fisher information, which enables to derive a closed form for a f…
In this paper, we focus on two different kinds of multipartite correlation, $k$-nonseparability and $k$-partite entanglement, both of which can describe the essential characteristics of multipartite entanglement. We propose effective methods to detect $k$-nonseparability and $k$-partite entanglement in terms of quantum Fisher information. We illustrate the significance of our results and show that they identify some $k$-nonseparability and $k$-partite entanglement that cannot be identified by known criteria by several concrete examples.
Extremal properties of the variance and the quantum Fisher information
我们表明，方差是自己的凹屋顶。对于秩为2的密度矩阵和密度矩阵的本征基中对角元素为零的算子，我们解析地证明了量子费舍尔信息是方差凸屋顶的4倍。强有力的数值证据表明，这一说法是真实的，甚至对运营商与非零对角元素或密度矩阵的秩大于2。我们还发现，在[D. Petz，J.Phys.A：Math.Gen.35，929（2002）; P. Gibilisco，F. Hiai和D. Petz，IEEE Trans. Inf. Theory 55，439（2009）]，在适当的归一化之后，量子费舍尔信息是最大的。因此，我们推测，即使在一般情况下，量子费舍尔信息也是方差凸屋顶的四倍。
The eigenstate thermalization hypothesis as well as the quantum ergodic theorem are studied in the light of quantum Fisher information. We show how global bounds on quantum Fisher information set the ETH and ergodicity conditions. Complexity and operator growth are briefly discussed in this frame.
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strate…
The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite entanglement is present. Recent results have related the quantum Fisher information to experimentally measurable probes. While in principle possible, a direct evaluation of the quantum Fisher information at finite temperatures is technically challenging and here we show that a simple estimate can be obtained for materials where the single mode approximation…
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occurs. The present study is relevant to quantum information processing and precision spectroscopy.
We show that two quantities in quantum metrology that were thought to be the same, the quantum Fisher information matrix and the Bures metric, are not the same. They differ at points at which the rank of the density matrix changes. The quantum Fisher information matrix is discontinuous at these points. However, these discontinuities are removable in some sense. We show that the expression given by the Bures metric represents the continuous version of the quantum Fisher information matrix. We also derive an explicit formula for the Bures metric for both singular and non-singular density matrice…
We develop a Bloch vector representation of Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and Skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and Skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping as well as the squeezed generalized amplitude damping…
