Related papers: Estimation of pure qubit states with collective an…
We discuss single adaptive measurements for the estimation of mixed quantum states of qubits. The results are compared to the optimal estimation schemes using collective measurements. We also demonstrate that the advantage of collective…
We propose practical and efficient protocols for verifying bipartite pure states for any finite dimension, which can also be applied to fidelity estimation. Our protocols are based on adaptive local projective measurements with either…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
A new qubit tomography protocol is introduced, based on a continuous positive operator valued measure, which is supported by the set of pure states, and equivariant under the symmetry group SO(3,R) of the qubit state space. Thus the sample…
The central problem of quantum statistics is to devise measurement schemes for the estimation of an unknown state, given an ensemble of $n$ independent identically prepared systems. For locally quadratic loss functions, the risk of standard…
Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements…
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement…
Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections.…
We propose a quantum device that can approximate any projective measurement on a qubit. The desired measurement basis is selected by the quantum state of a "program register". The device is optimized with respect to maximal average fidelity…
We demonstrate how to universally simulate ensemble statistics of projective local measurements on any $n$-qubit state shared among $n$ observers with classical communication and shared randomness. Our technique originates from protocols…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the…
In a recent work [Phys. Rev. Lett. 120, 170502 (2018)], Pallister et al. proposed an optimal strategy to verify non-maximally entangled two-qubit pure states under the constraint that the accessible measurements being locally projective and…
In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques.…
We present a method to estimate the probabilities of outcomes of a quantum observable, its mean value, and higher moments by measuring any other observable. This method is general and can be applied to any quantum system. In the case of…
We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that contrary to the impossibility of…
Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…