Quantum correlations may be measured by means of the distance of the state to the subclass of states $Ω$ having well defined classical properties. In particular, a geometric measure of asymmetric discord [Dakic et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance of a given two-qubit state to the closest classical-quantum (CQ) correlated state. We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance of a given state to the closest classical-classical (CC) correlated state. The optimal member of $Ω$ is just specially measured original state both for the CQ and CC discords. This implies that this measure is equal to quantum deficit of post-measurement purity. We discuss some general relations between the CC discords and explain why an analytical formula for the CC discord, contrary to the CQ discord, can hardly be found even for a general two-qubit state. Instead of such exact formula, we find simple analytical measurement-based upper bounds for the CC discord which, as we show, are very efficient in the case of two qubits and may serve as independent indicators of two-party quantum correlations. In particular, we propose an adaptive upper bound, which corresponds to the optimal states induced by single-party measurements: optimal measurement on one of the parties determines an optimal measurement on the other party. We discuss how to refine the adaptive upper bound by nonoptimal single-party measurements and by an iterative procedure which usually rapidly converges to the CC discord. We also raise the question of optimality of the symmetric measurements realising the CC discord on symmetric states, and give partial answer for the qubit case.
In this work we derive analytical relations between Entanglement and Coherence as well as between Discord and Coherence, for Bell-diagonal states and for X states, evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. We demonstrate that for these families, Coherence is the fundamental correlation, that is: Coherence is necessary for the presence of Entanglement and Discord.
The Generalized Werner-Like states (GWLs) are a class of non--X states in which the exchange operator is replaced for a generic one-rank projector in the Werner states. We obtained an exact analytical expression of Quantum Discord for these states. The optimization problem involved is solved by giving an analytical expression, in exact form for the conditional entropy. We compared the Quantum Discord (QD) with the Entanglement of Formation (EoF) for the same states. The pure states of GWLs with equal concurrence have the same QD and EoF.
Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy based classical correlation and von Neumann entropy based classical correlation. We present analytical formulae of linear entropy based classical correlation for arbitrary $d\otimes 2$ quantum states and von Neumann entropy based classical correlation for arbitrary $2\otimes 2$ rank-2 quantum states. From the von Neumann entropy based classical correlation, we d…
We obtained analytical expressions for Entangled of Formation (EoF) and Quantum Discord (QD) of Werner states and Generalized Werner-Like states. The optimization problem involved under the exact analytical form is obtained for both quantities. In order to illustrate the importance of our results we studied the EoF and the QD of these states. Using discrete formulation of continue states with the $f-$deformed coherent states obtained as deformed annihilation operator coherent states and as deformed displacement operator coherent states. The EoF and QD of bipartite Werner-Like states $f-$deform…
We present analytical and numerical simulation results for squeezing, entanglement, and quantum discord in a dissipatively coupled coherent Ising machine (CIM). Both analytical solutions and numerical simulation results, which are obtained with positive-P, truncated-Wigner and truncated-Husimi representations for the density operator, predict the presence of entanglement and quantum discord, below and above the threshold of CIM. The entanglement criteria and quantum discord are evaluated as a function of the dissipative coupling strength relative to the background loss. For coupled two DOPOs, …
Quantum discord is an effective measure of quantum correlation introduced by Olliver and Zurek. We evaluate analytically the quantum discord for a large family of non-X-states. Exact solutions of the quantum discord are obtained of the four parametric space for non-X-states. Dynamic behavior of the quantum discord is also explored under the action of the Kraus operator.
几何量子不和谐，由Dakic，Vedral和Brukner提出[Phys. Rev. Lett. 105（2010）190502]是二分相关性的重要度量。在本文中，我们将它推广到多体态，我们称之为广义几何整体量子不和谐（GGQD）。我们用不同的方法描述了GGQD，并给出了一些允许分析GGQD的特殊状态。
We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three-qubits and five-qubits is the same, as is the quantum discord of two-qubits and six-qubits. We discover that the quantum discord of this family states can be concluded into three categories. The level surfaces of the quantum discord in the three categories is shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord doesn…
Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit s…
Quantum Discord (QD) is a measure of the total quantum non-local correlations of a quantum system. The formalism of quantum discord has been applied to various two-qubit mixed states and it has been reported that there is a non-zero quantum discord even when the states are unentangled. To this end, we have calculated the Quantum Discord for higher than two qubit mixed state, that is, the generalized n-qubit Werner state with a bipartite split. We found that the QD saturates to a straight line with unit slope in the thermodynamic limit. Qualitative studies of entanglement between the two subsys…
Machine learning has achieved success in many areas because of its powerful fitting ability, so we hope it can help us to solve some significant physical quantitative problems, such as quantum correlation. In this research we will use neural networks to predict the value of quantum discord. Quantum discord is a measure of quantum correlation which is defined as the difference between quantum mutual information and classical correlation for a bipartite system. Since the definition contains an optimization term, it makes analytically solving hard. For some special cases and small systems, such a…
