Related papers: Adaptive quantum state tomography improves accurac…
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…
Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent…
Quantum physics constrains the accuracy of joint measurements of incompatible observables. Here we test tight measurement-uncertainty relations using single photons. We implement two independent, idealized uncertainty-estimation methods,…
We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consists of a number N of identically prepared qubits. We show that the average fidelity of the…
We introduce and experimentally demonstrate a technique for performing quantum state tomography on multiple-qubit states despite incomplete knowledge about the unitary operations used to change the measurement basis. Given unitary…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a…
We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the…
Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states,…
We show that quantum state tomography with perfect knowledge of the measurement apparatus proves to be, in some instances, inferior to strategies discarding all information about the measurement at hand, as in the case of data pattern…
This paper reconsiders the method of adaptive measurement for qubit state preparation developed by Jacobs and shows an alternative scheme that works even under unknown unitary evolution of the state. The key idea is that the measurement is…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We…
We demonstrate a fast, robust and non-destructive protocol for quantum state estimation based on continuous weak measurement in the presence of a controlled dynamical evolution. Our experiment uses optically probed atomic spins as a…
In this paper, we examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum state tomography. We find that, in some important circumstances, an elaborate…
Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the…