Discord, Quantum Correlations and Bell-type Inequality for Multi-qubit Systems

Indranil Chakrabarty, Subhashish Banerjee, Nana Siddharth

In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

Jianming Zhou, Xiaoli Hu, Naihuan Jing

Indranil Chakrabarty, Subhashish Banerjee, Nana Siddharth

In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

王仲宵, 王波波

You-neng Guo, Ke Zeng, Guo-You Wang

Palash Pandya, Avijit Misra, Indranil Chakrabarty

We find a single parameter family of genuinely entangled three-qubit pure states, called the maximally Bell-inequality violating states (MBV), which exhibit maximum Bell-inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so-called tangle measure. This in turn implies that there holds a complementary relation between the Bell-inequality violation by the reduced bipartite systems and the tangle present in the three-qubit states, not necessarily pure. The MBV states also exhibit maximum Bell-inequality violation by the reduced bipartite systems of the three-qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information-theoretic paradigm. The aforementioned complementary relation has also been established for three-qubit pure states for the generalized geometric measure and the discord monogamy score, respectively. The complementarity between the Bell-inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell-inequality violation in the reduced two-qubit system comes at the cost of the total tripartite correlation present in the entire system.