On Estimating the State of a Finite Level Quantum System

Estimating the expectation values of spin 1/2 observables with finite resources

We examine the problem of estimating the expectation values of two observables when we have a finite number of copies of an unknown qubit state. Specifically we examine whether it is better to measure each of the observables separately on different copies or to perform a joint measurement of the observables on each copy. We find that joint measurements can sometimes provide an advantage over separate measurements, but only if we make estimates of an observable based solely on the results of measurements of that observable. If we instead use both sets of results to estimate each observable then…

Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes

Determining the energy levels of a quantum system is a significant task, for instance, to analyze reaction rates in drug discovery and catalysis or characterize the compatibility of materials. In this paper we exploit quantum metrology, the research field focusing on the estimation of unknown parameters exploiting quantum resources, to address this problem for a three-level system interacting with laser fields. The performance of simultaneous estimation of the levels compared to independent one is also investigated in various scenarios. Moreover, we introduce, the Hilbert-Schmidt speed (HSS), …

通过簇级光锥分解估计局部可观测量

Estimating Local Observables via Cluster-Level Light-Cone Decomposition

本文提出基于簇级光锥分解的框架，通过因果解耦和代数分解算法，实现模拟成本与系统规模解耦，用于近期量子设备的局部物理探测。

有限尺寸光学晶格钟在估计引力势中的标准量子极限

Standard quantum limit of finite-size optical lattice clock in estimating gravitational potential

本文利用量子Cramér--Rao界研究有限尺寸光学晶格钟估计引力势的精度极限，发现引力退相导致估计精度随时间非单调变化并产生精度极限，且该极限在层数足够多时与晶格钟细节无关。

Estimating the privacy of quantum-random numbers

We analyze the information an attacker can obtain on the numbers generated by a user by measurements on a subsystem of a system consisting of two entangled two-level systems. The attacker and the user make measurements on their respective subsystems, only. Already the knowledge of the density matrix of the subsystem of the user completely determines the upper bound on the information accessible to the attacker. We compare and contrast this information to the appropriate bounds provided by quantum state discrimination.

Efficient Quantum Algorithms for Estimating Gauss Sums

We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we also give evidence that this problem is hard for classical algorithms. The workings of the quantum algorithm rely on the interaction between the additive characters of the Fourier transform and the multiplicative characters of the Gauss sum.