Multipartite fully entangled fraction

Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case, we call the generalized version multipartite fully entangled fraction (MFEF). MFEF measures the closeness of a state to GHZ states. The analytical expressions of MFEF are very difficult to obtain except for very special states, however, we show that, the MFEF of any state is determined by a system of finite-order polynomial equations. Therefore, the MFEF can be efficiently numerically computed.Comment: 5 pages, no figure. Any comments are welcome

Lazy states, discordant states and entangled states for 2-qubit systems

We investigate the lazy states, entangled states and discordant states for 2-qubit systems. We show that many lazy states are discordant, many lazy states are entangled, and many mixed entangled states are not lazy. With these investigations, we provide a laziness-discord-entanglement hierarchy diagram about 2-qubit quantum correlations.Comment: 4 pages, 1 figur

Oblique discord

Discord and entanglement characterize two kinds of quantum correlations, and discord captures more correlation than entanglement in the sense that even separable states may have nonzero discord. In this paper, we propose a new kind of quantum correlation we call it oblique discord. A zero-discord state corresponds to an orthonormal basis, while a zero-oblique-discord state corresponds to a basis which is not necessarily orthogonal. Under this definition, the set of zero-discord states is properly contained inside the set of zero-oblique-discord states, and the set of zero-oblique-discord states is properly contained inside the set of separable states. We give a characterization of zero-oblique-discord states via quantum operation, provide a geometric measure for oblique discord, and raise a conjecture with it holds we can define an information-theoretic measure for oblique discord. Also, we point out that, the definition of oblique discord can be properly extended to some different versions just as the case of quantum discord.Comment: 4 pages,1 figure. Comments are welcome

Global Quantum discord of multi-qubit states

Global quantum discord (GQD), proposed by Rulli and Sarandy [Phys. Rev. A \textbf{84}, 042109 (2011)], is a generalization of quantum discord to multipartite states. In this paper, we provide an equivalent expression for GQD, and obtain the analytical expressions of GQD for two classes of multi-qubit states. The phenomena of sudden transition and freeze of GQD are also discussed.Comment: 6 pages, 1 figure. Comments are welcom

Quantifying coherence of Gaussian states

Coherence arises from the superposition principle and plays a key role in quantum mechanics. Recently, Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] established a rigorous framework for quantifying the coherence of finite dimensional quantum states. In this work we provide a framework for quantifying the coherence of Gaussian states and explicitly give a coherence measure based on the relative entropy.Comment: 6 pages,no figur

Robustness of quantum discord to sudden death in NMR

We investigate the dynamics of entanglement and quantum discord of two qubits in liquid state homonuclear NMR. Applying a phenomenological description for NMR under relaxation process, and taking a group of typical parameters of NMR, we show that when a zero initial state $|00>$ experiences a relaxation process, its entanglement disappears completely after a sequence of so-called sudden deaths and revivals, while the quantum discord retains remarkable values after a sequence of oscillations. That is to say, the quantum discord is more robust than entanglement.Comment: 8 pages, 10 figures, single-colum

Database-assisted Distributed Spectrum Sharing

According to FCC's ruling for white-space spectrum access, white-space devices are required to query a database to determine the spectrum availability. In this paper, we study the database-assisted distributed white-space access point (AP) network design. We first model the cooperative and non-cooperative channel selection problems among the APs as the system-wide throughput optimization and non-cooperative AP channel selection games, respectively, and design distributed AP channel selection algorithms that achieve system optimal point and Nash equilibrium, respectively. We then propose a state-based game formulation for the distributed AP association problem of the secondary users by taking the cost of mobility into account. We show that the state-based distributed AP association game has the finite improvement property, and design a distributed AP association algorithm that can converge to a state-based Nash equilibrium. Numerical results show that the algorithm is robust to the perturbation by secondary users' dynamical leaving and entering the system

Spatial Spectrum Access Game

A key feature of wireless communications is the spatial reuse. However, the spatial aspect is not yet well understood for the purpose of designing efficient spectrum sharing mechanisms. In this paper, we propose a framework of spatial spectrum access games on directed interference graphs, which can model quite general interference relationship with spatial reuse in wireless networks. We show that a pure Nash equilibrium exists for the two classes of games: (1) any spatial spectrum access games on directed acyclic graphs, and (2) any games satisfying the congestion property on directed trees and directed forests. Under mild technical conditions, the spatial spectrum access games with random backoff and Aloha channel contention mechanisms on undirected graphs also have a pure Nash equilibrium. We also quantify the price of anarchy of the spatial spectrum access game. We then propose a distributed learning algorithm, which only utilizes users' local observations to adaptively adjust the spectrum access strategies. We show that the distributed learning algorithm can converge to an approximate mixed-strategy Nash equilibrium for any spatial spectrum access games. Numerical results demonstrate that the distributed learning algorithm achieves up to superior performance improvement over a random access algorithm.Comment: The paper has been accepted by IEEE Transactions on Mobile Computin

Evolutionarily Stable Spectrum Access

In this paper, we design distributed spectrum access mechanisms with both complete and incomplete network information. We propose an evolutionary spectrum access mechanism with complete network information, and show that the mechanism achieves an equilibrium that is globally evolutionarily stable. With incomplete network information, we propose a distributed learning mechanism, where each user utilizes local observations to estimate the expected throughput and learns to adjust its spectrum access strategy adaptively over time. We show that the learning mechanism converges to the same evolutionary equilibrium on the time average. Numerical results show that the proposed mechanisms are robust to the perturbations of users' channel selections.Comment: arXiv admin note: substantial text overlap with arXiv:1103.102

Imitation-based Social Spectrum Sharing

Dynamic spectrum sharing is a promising technology for improving the spectrum utilization. In this paper, we study how secondary users can share the spectrum in a distributed fashion based on social imitations. The imitation-based mechanism leverages the social intelligence of the secondary user crowd and only requires a low computational power for each individual user. We introduce the information sharing graph to model the social information sharing relationship among the secondary users. We propose an imitative spectrum access mechanism on a general information sharing graph such that each secondary user first estimates its expected throughput based on local observations, and then imitates the channel selection of another neighboring user who achieves a higher throughput. We show that the imitative spectrum access mechanism converges to an imitation equilibrium, where no beneficial imitation can be further carried out on the time average. Numerical results show that the imitative spectrum access mechanism can achieve efficient spectrum utilization and meanwhile provide good fairness across secondary users