Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHellinger distance as a measure of Gaussian discord
229
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Especially investigated in recent years, the Gaussian discord can be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of product states, such a distance captures all the correlations (quantum and classical) between modes. Therefore it is merely un upper bound for the geometric discord, no matter which is the employed distance. In this work we choose for this purpose the Hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour. In general, this metric is determined by affinity, a relative of the Uhlmann fidelity with which it shares many important features. As a first step of our work, the affinity of a pair of $n$-mode Gaussian states is written. Then, in the two-mode case, we succeeded in determining exactly the closest Gaussian product state and computed the Gaussian discord accordingly. The obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two-mode Gaussian states. We then analyze in detail two special classes of two-mode Gaussian states of theoretical and experimental interest as well: the squeezed thermal states and the mode-mixed thermal ones. The former are separable under a well-known threshold of squeezing, while the latter are always separable. It is worth stressing that for symmetric states belonging to either of these classes, we find consistency between their geometric Hellinger discord and the originally defined discord in the Gaussian approach. At the same time, the Gaussian Hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations.
rate research
Read More
We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was considerably simplified by using the remarkable properties of the Uhlmann fidelity as well as the standard form II of the covariance matrix of a symmetric state. Our result for the Gaussian degree of entanglement measured by the Bures distance depends only on the smallest symplectic eigenvalue of the covariance matrix of the partially transposed density operator. It is thus consistent to the exact expression of the entanglement of formation for symmetric two-mode Gaussian states. This non-trivial agreement is specific to the Bures metric.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.
A symmetric measure of quantum correlation based on the Hilbert-Schmidt distance is presented in this paper. For two-qubit states, we simplify considerably the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There is certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.
Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.
We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap and its relation to the Uhlmann fidelity are interestingly illustrated by our approach.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
