Quantum Correlations in Multipartite Quantum Systems

We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlationsComment: to be published as a chapter of the book "Lectures on general quantum correlations and their applications" edited by F. Fanchini, D. Soares-Pinto, and G. Adesso (Springer, 2017

Dynamics of multipartite quantum correlations under decoherence

Quantum discord is an optimal resource for the quantification of classical and non-classical correlations as compared to other related measures. Geometric measure of quantum discord is another measure of quantum correlations. Recently, the geometric quantum discord for multipartite states has been introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have investigated global quantum discord (QD) and geometric quantum discord (GQD) under the influence of external environments for different multipartite states. Werner-GHZ type three-qubit and six-qubit states are considered in inertial and non-inertial settings. The dynamics of QD and GQD is investigated under amplitude damping, phase damping, depolarizing and flipping channels. It is seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ states and for p>0.5 for six qubit GHZ states. This implies that multipartite states are more fragile to decoherence for higher values of N. Surprisingly, a rapid sudden death of discord occurs in case of phase flip channel. However, for bit flip channel, no sudden death happens for the six-qubit states. On the other hand, depolarizing channel heavily influences the QD and GQD as compared to the amplitude damping channel. It means that the depolarizing channel has the most destructive influence on the discords for multipartite states. From the perspective of accelerated observers, it is seen that effect of environment on QD and GQD is much stronger than that of the acceleration of non-inertial frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore, QD exhibits more robustness than GQD when the multipartite systems are exposed to environment.Comment: 15 pages, 4 figures, 4 table

Conditions for the freezing phenomena of geometric measure of quantum discord for arbitrary two-qubit X states under non-dissipative dephasing noises

We study the dynamics of geometric measure of quantum discord (GMQD) under the influences of two local phase damping noises. Consider the two qubits initially in arbitrary X-states, we find the necessary and sufficient conditions for which GMQD is unaffected for a finite period. It is further shown that such results also hold for the non-Markovian dephasing process.Comment: 4 pages, 2 figure

Structure and mechanism of acetolactate decarboxylase

Acetolactate decarboxylase catalyzes the conversion of both enantiomers of acetolactate to the (R)-enantiomer of acetoin, via a mechanism that has been shown to involve a prior rearrangement of the non-natural (R)-enantiomer substrate to the natural (S)-enantiomer. In this paper, a series of crystal structures of ALDC complex with designed transition state mimics are reported. These structures, coupled with inhibition studies and site-directed mutagenesis provide an improved understanding of the molecular processes involved in the stereoselective decarboxylation/protonation events. A mechanism for the transformation of each enantiomer of acetolactate is proposed

Sparsification Lower Bounds for List H-Coloring

We investigate the List H-Coloring problem, the generalization of graph coloring that asks whether an input graph G admits a homomorphism to the undirected graph H (possibly with loops), such that each vertex v ? V(G) is mapped to a vertex on its list L(v) ? V(H). An important result by Feder, Hell, and Huang [JGT 2003] states that List H-Coloring is polynomial-time solvable if H is a so-called bi-arc graph, and NP-complete otherwise. We investigate the NP-complete cases of the problem from the perspective of polynomial-time sparsification: can an n-vertex instance be efficiently reduced to an equivalent instance of bitsize ?(n^(2-?)) for some ? > 0? We prove that if H is not a bi-arc graph, then List H-Coloring does not admit such a sparsification algorithm unless NP ? coNP/poly. Our proofs combine techniques from kernelization lower bounds with a study of the structure of graphs H which are not bi-arc graphs

Poly(vinyl methyl ether) hydrogels at temperatures below the freezing point of water - molecular interactions and states of water

Water interacting with a polymer reveals a number of properties very different to bulk water. These interactions lead to the redistribution of hydrogen bonds in water. It results in modification of thermodynamic properties of water and the molecular dynamics of water. That kind of water is particularly well observable at temperatures below the freezing point of water, when the bulk water crystallizes. In this work, we determine the amount of water bound to the polymer and of the so-called pre-melting water in poly(vinyl methyl ether) hydrogels with the use of Raman spectroscopy, dielectric spectroscopy, and calorimetry. This analysis allows us to compare various physical properties of the bulk and the premelting water. We also postulate the molecular mechanism responsible for the pre-melting of part of water in poly(vinyl methyl ether) hydrogels. We suggest that above −60 °C, the first segmental motions of the polymer chain are activated, which trigger the process of the pre-melting

Poly(vinyl methyl ether) hydrogels at temperatures below the freezing point of water - molecular interactions and states of water

Water interacting with a polymer reveals a number of properties very different to bulk water. These interactions lead to the redistribution of hydrogen bonds in water. It results in modification of thermodynamic properties of water and the molecular dynamics of water. That kind of water is particularly well observable at temperatures below the freezing point of water, when the bulk water crystallizes. In this work, we determine the amount of water bound to the polymer and of the so-called pre-melting water in poly(vinyl methyl ether) hydrogels with the use of Raman spectroscopy, dielectric spectroscopy, and calorimetry. This analysis allows us to compare various physical properties of the bulk and the premelting water. We also postulate the molecular mechanism responsible for the pre-melting of part of water in poly(vinyl methyl ether) hydrogels. We suggest that above −60 °C, the first segmental motions of the polymer chain are activated, which trigger the process of the pre-melting

Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105,190502 (2010)] who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu [Phys. Rev. A \textbf{82}, 034302 (2010)] introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in a N-qubit quantum state. The exact formulas for the $N$-qubit quantum state are experimentally implementable.Comment: 18 pages, 3 figure

Geometric global quantum discord

Geometric quantum discord, proposed by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502], is an important measure for bipartite correlations. In this paper, we generalize it to multipartite states, we call the generalized version geometric global quantum discord (GGQD). We characterize GGQD in different ways, and provide some special states which allow analytical GGQD.Comment: 8 pages,no figure;added a lower bound for GGQD to version