Asymptotic estimation of shift parameter of a quantum state

Asymptotic Quantum Parameter Estimation in Spin 1/2 System

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.

Asymptotic estimation theory for a finite dimensional pure state model

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.

通过广义量子比特化实现渐近最优的量子振幅估计

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。

Quantum Phase Estimation with Arbitrary Constant-precision Phase Shift Operators

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase pr…

Experimental quantum-enhanced estimation of a lossy phase shift

When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate Heisenberg limit on precision, but at the same time are extremely fragile to losses. In contrast, we provide experimental evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation when losses are present.

利用自旋压缩态进行渐近最优的相位和退相位强度联合估计

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。

Asymptotic quantum estimation theory for the displaced thermal states family

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.

Optimal estimation of conjugate shifts in position and momentum by classically correlated probes and measurements

Multi-parameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position and momentum. Designing quantum probes that allow simultaneous estimation of all parameters is therefore an important task. The optimal methods for estimation of the conjugate changes of position and momentum of quantum harmonic oscillator employ probes in entangled or quantum non-Gaussian states. We show that the same results can be obtained in a significantly more feasible fashion by employing independent sets of differently squeezed Gaussian states classically correlated to…

On the general problem of quantum phase estimation

The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two relevant examples are analyzed: i) a multi-mode phase shift operator for multipath interferometry; ii) the two mode heterodyne phase detection.

二次和三次散射在两个连续相位移估计中的应用

Quadratic and cubic scrambling in the estimation of two successive phase-shifts

本文研究了二次和三次非线性散射在两个连续相位移估计中的应用，发现三次非线性在提升估计精度方面优于二次非线性，并展示了联合估计在特定条件下的优势。

Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems

We apply the recent results of F. Hiai, M. Mosonyi and T. Ogawa [arXiv:0707.2020, to appear in J. Math. Phys.] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasi-free states on a CAR algebra. We use a multivariate extension of Szego's theorem to show the existence of the mean Chernoff and Hoeffding bounds and the mean relative entropy, and show that these quantities arise as the optimal error exponents in suitable settings.

Real-time estimation of the optically detected magnetic resonance shift in diamond quantum thermometry

We investigate the real-time estimation protocols for the frequency shift of optically detected magnetic resonance (ODMR) of nitrogen-vacancy (NV) centers in nanodiamonds (NDs). Efficiently integrating multipoint ODMR measurements and ND particle tracking into fluorescence microscopy has recently demonstrated stable monitoring of the temperature inside living animals. We analyze the multipoint ODMR measurement techniques (3-, 4-, and 6-point methods) in detail and quantify the amount of measurement artifact owing to several systematic errors derived from instrumental errors of experimental har…

Multiparameter quantum estimation of noisy phase shifts

Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a multiparameter approach, in which noise is associated to a parameter to be measured at the same time as the phase. We present an experiment using two-photon states, and apply our setup to investigating optical activity of fructose solutions. Finally, we illustrate the scaling laws of the attainable precisions with the number of photons in the probe state.