Hierarchy of quantum correlation measures for two-qubit X states
Year: 2013
Type: preprint
Abstract: Generalized quantum discord $(D_q)$, entanglement $(E)$, steering $(S_n^{v,e})$, and Bell nonlocality ($\mathcal{N}$) are logically distinct quantifiers of quantum correlations. All these measures capture some nonclassical aspect of quantum states and play some role as resources in quantum information processing. In this paper we look for a possible hierarchy among these quantum correlation witnesses for a given class of two-qubit states. We start by providing formal measures which are in agreement with current knowledge. Then, we show that $(\tfrac{2^q\ln 2}{q}D_q)^{1/2}\geq E\geq \mathcal{N} \geq S_2^e\leq S_3^e\leq E$, whereas there is not such a clear hierarchy as far as the variance-based steering $S_{2,3}^v$ is concerned. In addition, we prove by example that $S_{2,3}^v$ is not {\em invariant} under local unitary operations, being therefore not suitable for quantifying quantum correlations. Finally, since the observed hierarchy maintains when the quantum states under concern are subjected to certain noisy quantum channels, we derive a related chronology for sudden deaths.
Source: arXiv (Cornell University)
Authors: Ana C. S. Costa, R. M. Angelo, Marcus W. Beims
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1515634767