Masahito Hayashi
For the precise estimation of the unknown quantum state, the independent samples should be prepared. Can we reduce the error of the estimation by the measurement using the quantum correlation between every sample? In this paper, this question is treated in the parameter estimation for the unknown state.
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We give a rigorous treatment on the foundation of the first order asymptotic theory of quantum estimation, with tractable and reasonable regularity conditions. Different from past works, we do not use Fisher information nor MLE, and an optimal estimator is constructed based on locally unbiased estimators. Also, we treat state estimation by local operations and classical communications (LOCC), and estimation of quantum operations.
The impossibility of perfect cloning and state estimation are two fundamental results in Quantum Mechanics. It has been conjectured that quantum cloning becomes equivalent to state estimation in the asymptotic regime where the number of clones tends to infinity. We prove this conjecture using two known results of Quantum Information Theory: the monogamy of quantum correlations and the properties of entanglement breaking channels.
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show that this bound of such a model cannot be attained by any quantum measurement with no quantum correlation in the measuring apparatus. That is, in such a model, the quantum correlation can improve the accuracy of the estimation in an asymptotic setting.
The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample.
Asymptotically Optimal Quantum Amplitude Estimation by Generalized Qubitization
该研究证明量子振幅估计的标准差误差渐近下界约为1.28倍查询次数的倒数，提出可同时块编码多个多项式的广义量子比特化方法，实现了最优渐近精度，验证了下界的紧性。
Asymptotically optimal joint phase and dephasing strength estimation using spin-squeezed states
本文提出一种涉及一轴扭曲自旋压缩态的N量子比特协议，实现相位和退相位强度的联合估计，其精度渐近接近量子计量基本界限。
Concerning state estimation, we will compare two cases. In one case we cannot use the quantum correlations between samples. In the other case, we can use them. In addition, under the later case, we will propose a method which simultaneously measures the complex amplitude and the expected photon number for the displaced thermal states.
We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing literature on frequentist quantum estimation has not rigorously examined the finite sample performance of the estimators and associated methods of hypothesis testing. While ML is usually preferred on the basis of its asymptotic properties - it achieves the Cramer-Rao (CR) lower bound - the finite sample properties are often less than optimal. We compare the…
Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework
本文证明概率估计框架的渐近最优性，刻画无信令与量子受限对抗攻击，并展示其在 Bell 场景中的鲁棒性。
The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. In quantum metrology, people are interested in calculating the QFI of $N$ identical copies of a quantum channel when $N \rightarrow \infty$, which is called the asymptotic QFI. Over the years, researchers found various types of upper bounds of the asymptotic QF…
Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understandin…
We propose a state estimation scheme for spins, using a modified setup of the Stern-Gerlach experiment, in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed linear inversion estimation procedure, based on a quadrant intensity detector, requires a suitable initial spatial state of the beam. The statistical characterization of the estimator of the initial spin state allows us not only to associate an error to the estimated parameters, but also to define a measure for comparing estimation procedures corresponding to different Stern-Gerlach …
We study the estimation of an infinitesimal rotation of a spin-j system, characterized by two unknown phases, and compare the estimation precision achievable with two different strategies. The first is a standard `joint estimation' strategy, in which a single probe state is used to estimate both parameters, while the second is a `sequential' strategy in which the two phases are estimated separately, each on half of the total number of system copies. In the limit of small angles we show that, although the joint estimation approach yields in general a better performance, the two strategies posse…
We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of estimation of shift parameter in Sec. 2, we study the structure of the optimal covariant estimate in Sec. 3, showing how entanglement comes into play for several independent trials. In Secs. 4,5 we give the asymptotics of the performance of the optimal covariant estimate comparing it with the ``semiclassical'' unentangled covariant estimation in the regular ca…
We consider spin-half fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square well potential. We derive the analytic form of the asymptotic wave-functions at short range of two fermions in the subspace of zero net momentum and zero total angular momentum. We show that the spin-orbit coupling has perturbative effects on the short range asymptotic behavior of the wave-functions away from resonances. We argue that our conclusion should hold generally.
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