Detecting coherence via spectrum estimation

Abstract

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to measure the coherence in experiments limits the applications. We address this problem by introducing an experiment-friendly method for coherence and spectrum estimation. This method is based on the theory of majorization and can not only be used to prove the presence of coherence, but also result in a rather precise lower bound of the amount of coherence. As an illustration, we show how to characterize the freezing phenomenon of coherence with only two local measurements for any N-qubit quantum systems. Our approach also has other applications in quantum information processing, such as the characterization of distillability and entanglement transformations. * Xiao-Dong.Yu@uni-siegen.de † otfried.guehne@uni-siegen.de

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

“…For such systems, a spectrum‐based estimation method was proposed in ref. [116] which can be used to provide bounds for coherence measures such as the robustness of coherence , the relative entropy of coherence , or the ℓ 1 ‐norm of coherence . The crucial aspect of this scheme is that a small number of local measurements can suffice to provide useful bounds.…”

The Tightness of Multipartite Coherence from Spectrum Estimation

“…Efficient protocols for detecting quantum coherence without quantum state tomography have been recently investigated [38][39][40][41][42][43][44][45][46]. However, the initial proposals require either complicated experimental settings for multipartite quantum systems [38][39][40] or complex numerical optimizations [41].…”

“…However, the initial proposals require either complicated experimental settings for multipartite quantum systems [38][39][40] or complex numerical optimizations [41]. An experiment-friendly tool, the so-called spectrum-estimationbased method, requires local measurements and simple post-processing [42], and has been experimentally demonstrated to measure the relative entropy of coherence [43]. Other experiment-friendly tools, such as the fidelity-based estimation method [44] and the witness-based estimation method [46], have been successively proposed very recently.…”

“…Still, there are several unexplored matters along this line of research. First, on the theoretical side, although it has been studied that the spectrum-estimation-based method is capable of detecting the coherence of several coherence measures [42], there still exists some coherence measures that are unexplored. On the experimental side, the realization is focused on the detection of relative entropy of coherence [43], and its feasibility for other coherence measures has not been tested.…”

Optimal common resource in majorization-based resource theories

“…Before doing that, we stress that the lattice theoretical aspects of majorization theory have not been sufficiently exploited in comparison with other features of it in the area of quantum information. Indeed, the first applications were given in [30,31]; only recently, new applications of the majorization lattice have been found [32][33][34][35][36][37][38][39].…”