We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of identically prepared systems. We illustrate the general formalism by applying it to different scenarios of the state estimation of N independent and identically prepared two-level systems (qubits).
Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation.
We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data-processing of the outcomes of a quantum measurement described by a POVM. After reviewing the optimization of data processing that minimizes the statistical error of the estimation, we provide a compact formula for the evaluation of the estimation error.
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity. We use the two-qubit encoding and swapping-based operations to simplify a physical realization of universal quantum computing and add the immunity to a number of errors. This approach allows to implement any encoded single-qubit operation by three elementary gates and the encoded controlled- NOT operation can be performed in a single step. The considerable a…
We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state non-deterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$-interaction, using $\ceil*{\log_2 N} + 1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamon…
Multiparameter estimation, which aims to simultaneously determine multiple parameters in the same measurement procedure, attracts extensive interests in measurement science and technologies. Here, we propose a multimode many-body quantum interferometry for simultaneously estimating linear and quadratic Zeeman coefficients via an ensemble of spinor atoms. Different from the scheme with individual atoms, by using an $N$-atom multimode GHZ state, the measurement precisions of the two parameters can simultaneously attain the Heisenberg limit, and they respectively depend on the hyperfine spin numb…
In analogy with the usual state estimation problem, we introduce the problem of state estimation for a pre- and post-selected ensemble. The problem has fundamental physical significance since, as argued by Y. Aharonov and collaborators, pre- and post-selected ensembles are the most basic quantum ensembles. Two new features are shown to appear: 1) information is flowing to the measuring device both from the past and from the future; 2)because of the post-selection, certain measurement outcomes can be forced never to occur. Due to these features, state estimation in such ensembles is dramaticall…
It is shown that excitation spectra of Generalized Gibbs Ensembles (GGE) of one-dimensional integrable models with isotopic symmetry contain universal features insensitive to details of the distribution. Namely, the low energy limit of the subsystem of isotopic (for instance, spin) excitations is described by the effective action of a ferromagnet at thermodynamic equilibrium with a single temperature and with the stiffness determined by the initial conditions. The condition of universality is that the entropy per excited particle is small.
Optical depth dictates universal bounds on many-body decay in atomic ensembles
Instituto de Física Fundamental - Consejo Superior de Investigaciones Científica (CSIC)（基础物理研究所 - 西班牙国家研究委员会）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Department of Physics, Harvard University（哈佛大学物理系）；Physikalisches Institut, University of Bonn（波恩大学物理研究所）
We study the collective excitation of a macroscopic ensemble of polarized nuclei fixed in a quantum dot. Under the approximately homogeneous condition that we explicitly present in this paper, this many-particle system behaves as a single mode boson interacting with the spin of a single conduction band electron confined in this quantum dot. Within this effective spin-boson system, the quantum information carried by the electronic spin can be coherently transferred into the collective bosonic mode of excitation in the ensemble of nuclei. In this sense, the collective bosonic excitation can serv…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon…
Nature is stingy: Universality of Scrooge ensembles in quantum many-body systems
California Institute of Technology（加州理工学院）；Technology Innovation Institute（技术创新研究所）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）
