Optimal verification of entangled states with local measurements

Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or alternatively to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal amongst local verification strategies for two qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, non-adaptive and non-collective measurements only incurs a constant-factor penalty over a strategy without these restrictions.Comment: Document includes supplemental material. Main paper: 5 pages, 2 figs; supplemental material: 16 pages, 2 fig

Rayleigh estimates: performing like SVD

This paper describes the structure of the so- called Rayleigh estimates and the features they share with indirect SVD like procedures. The problem of finding procedures of high resolution in spectral estimation is faced under the framework of non-linear estimates of the autocorrelation matrix and the low rank approximation to the frequency estimation problem. It is shown the existing relations hip between the proposed estimates and the principal component analysis. The main advantages of the procedure is that the performance of the spectral estimates reported herein is almost equal to SVD techniques, yet preserving a good asymptotic convergence to the actual power spectral density. Also, the procedure could be viewed under variotional concepts revealing its potential under adaptive schemes and data adaptive windowing for spectral estimation. In summary, the work shows how classical constrained Wiener filtering with data adaptive windowing can enhance the performance of SVD met hods with very low complexity.Peer ReviewedPostprint (published version

Incoherent Frequency Fusion for Broadband Steered Response Power Algorithms in Noisy Environments

The steered response power (SRP) algorithms have been shown to be among the most effective and robust ones in noisy environments for direction of arrival (DOA) estimation. In broadband signal applications, the SRP methods typically perform their computations in the frequency-domain by applying a fast Fourier transform (FFT) on a signal portion, calculating the response power on each frequency bin, and subsequently fusing these estimates to obtain the final result. We introduce a frequency response incoherent fusion method based on a normalized arithmetic mean (NAM). Experiments are presented that rely on the SRP algorithms for the localization of motor vehicles in a noisy outdoor environment, focusing our discussion on performance differences with respect to different signal-to-noise ratios (SNR), and on spatial resolution issues for closely spaced sources. We demonstrate that the proposed fusion method provides higher resolution for the delay-and-sum SRP, and improved performances for minimum variance distortionless response (MVDR) and multiple signal classification (MUSIC