On fairness,full cooperation,and quantum game with incomplete information

Quantum entanglement has emerged as a new resource to enhance cooperation and remove dilemmas. This paper aims to explore conditions under which full cooperation is achievable even when the information of payoff is incomplete.Based on the quantum version of the extended classical cash in a hat game, we demonstrate that quantum entanglement may be used for achieving full cooperation or avoiding moral hazards with the reasonable profit distribution policies even when the profit is uncertain to a certain degree. This research further suggests that the fairness of profit distribution should play an important role in promoting full cooperation. It is hopeful that quantum entanglement and fairness will promote full cooperation among distant people from various interest groups when quantum networks and quantum entanglement are accessible to the public.     

Entanglement Degree of Finite-Dimensional Pair Coherent States

We study in detail the entanglement degree of finite-dimensional pair coherent states (PCSs) in terms of different parameters involved in the coherent states. Since these states are a type of correlated two-mode states in finite dimension, we use the D concurrence and linear entropy to quantify their amount of entanglement. We show that the maximum entanglement can be obtained for two and threedimensional (finite-dimensional) PCSs, and states with higher dimensions cannot attain this limit. We generalize the discussion to a superposition of two states of this class and give the maximum entangled states for even and odd finite-dimensional PCSs. In addition, we consider the entanglement degree of nonlinear finite-dimensional PCSs and survey the maximality condition. Finally, we discuss the entanglement for a class of mixed states defined as a statistical mixture of two pure finite-dimensional PCSs. Our observations may have important implications in exploiting these states in quantum information theory.     

Degree of Entanglement for Some Bipartite Entangled Bosonic Systems

We calculate the degree of entanglement for some bipartite entangled states of continuous variables.These states include common two-mode squeezed vacuum state, thermal vacuum state of a free single particle (where theh fictitious tilde system is regarded as another particle), and the squeezed vacuum state of two coupling harmonic oscillators.The degree of entanglement for these quantum systems are shown clearly by using the technique of integration within an ordered product of operators.     

Degree of Entanglement for Some Bipartite Entangled Bosonic Systems

We calculate the degree of entanglement for some bipartite entangled states of continuous variables.These states include common two-mode squeezed vacuum state, thermal vacuum state of a free single particle (where the fictitious tilde system is regarded as another particle), and the squeezed vacuum state of two coupling harmonic oscillators.The degree of entanglement for these quantum systems are shown clearly by using the technique of integration within an ordered product of operators.     

Entanglement Degree of Parasupersymmetric Coherent States of Harmonic Oscillator

We study the boson–parafermion entanglement of the parasupersymmetric coherent states of the harmonic oscillator and derive the degree of entanglement in terms of the concurrence. The conditions for obtaining the maximal entanglement is also examined, and it is shown that in the usual supersymmetry situation we can obtain maximally entangled Bell states. PACS numbers: 03.67.Ud 03.67.Mn     

Emergence of fairness in repeated group interactions

Often groups need to meet repeatedly before a decision is reached. Hence, most individual decisions will be contingent on decisions taken previously by others. In particular, the decision to cooperate or not will depend on one's own assessment of what constitutes a fair group outcome. Making use of a repeated N-person prisoner's dilemma, we show that reciprocation towards groups opens a window of opportunity for cooperation to thrive, leading populations to engage in dynamics involving both coordination and coexistence, and characterized by cycles of cooperation and defection. Furthermore, we show that this process leads to the emergence of fairness, whose level will depend on the dilemma at stake.     

基于纠缠度计算的量子移动信令相邻小区越区切换策略及仿真

信令是任何通信系统必不可少的重要组成部分,量子移动通信也不例外.然而,关于量子移动通信信令在相邻小区越区切换过程中的切换策略问题的研究迄今尚未展开.随着移动用户位置的改变,用户与基站间的纠缠度不断变化.本文提出了基于纠缠度计算的量子信令在相邻小区的越区切换策略.首先定义了信令纠缠度与距离的关系,然后研究了用户位置改变所导致用户与基站之间信令纠缠度的变化情况,提出了基于纠缠度阈值计算的切换算法.仿真结果表明,本文所提出的信令切换策略可靠性高,能够在各基站之间实现平稳切换.因此,本研究对于构造量子移动通信网络的信令系统及其标准的制定具有极为重要的技术支撑作用.     

Efficient Polarization Entanglement Distribution for W State Assisted by Frequency Degree of Freedom

We present an efficient faithful polarization entanglement distribution protocol for W state over an arbitrary noise channel,which use the frequency degree of freedom to carry the entanglement during the transmission.We describe the transmission of three-photon W state as an example,and then generalize this scheme to n-qubit W state situation.The remote parties can obtain maximally entangled W states on the polarization of photons,and the success probability is 100% in principle.As there was few entanglement purification for W state,our scheme is an efficient and practical method to share W state entanglement between distant parties,which will be useful in quantum communication.We also show that our scheme can be used to distribute arbitrary multi-particle entangled state.     

基于纠缠度计算的量子移动信令相邻小区越区切换策略及仿真

信令是任何通信系统必不可少的重要组成部分,量子移动通信也不例外.然而,关于量子移动通信信令在相邻小区越区切换过程中的切换策略问题的研究迄今尚未展开.随着移动用户位置的改变,用户与基站间的纠缠度不断变化.本文提出了基于纠缠度计算的量子信令在相邻小区的越区切换策略.首先定义了信令纠缠度与距离的关系,然后研究了用户位置改变所导致用户与基站之间信令纠缠度的变化情况,提出了基于纠缠度阈值计算的切换算法.仿真结果表明,本文所提出的信令切换策略可靠性高,能够在各基站之间实现平稳切换.因此,本研究对于构造量子移动通信网络的信令系统及其标准的制定具有极为重要的技术支撑作用.     

Prisoner's Dilemma Game on Two Types of Positively Correlated Networks

We study the effects of degree correlations on the evolution of cooperation in the prisoner＇s dilemma game with individuals located on two types of positively correlated networks. It is shown that the positive degree correlation can either promote or inhibit the emergence of cooperation depending on network configurations. Furthermore, we investigate the probability to cooperate as a function of connectivity degree, and find that high-degree individuals generally have a higher tendency to cooperate. Finally, it is found that small-degree individuals usually change their strategy more frequently, and such change is shown to be unfavourable to cooperation for both kinds of networks.     

Coevolutionary,coexisting learning and teaching agents model for prisoner’s dilemma games enhancing cooperation with assortative heterogeneous networks

Unlike other natural network systems, assortativity can be observed in most human social networks, although it has been reported that a social dilemma situation represented by the prisoner’s dilemma favors dissortativity to enhance cooperation. We established a new coevolutionary model for both agents’ strategy and network topology, where teaching and learning agents coexist. Remarkably, this model enables agents’ enhancing cooperation more than a learners-only model on a time-frozen scale-free network and produces an underlying assortative network with a fair degree of power-law distribution. The model may imply how and why assortative networks are adaptive in human society.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

Influence of the variance of degree distributions on the evolution of cooperation in complex networks

We study how initial network structure affects the evolution of cooperation in a spatial prisoner’s dilemma game. The network structure is characterized by various statistical properties. Among those properties, we focus on the variance of the degree distribution, and inquire how it affects the evolution of cooperation by three methods of imitation. For every method, it was found that a scale-free network does not always promote the evolution of cooperation, and that there exists an appropriate value of the variance, at which cooperation is optimal.     

Effects of average degree on cooperation in networked evolutionary game

We study effects of average degree on cooperation in the networked prisoner's dilemma game. Typical structures are considered, including random networks, small-world networks and scale-free networks. Simulation results show that the average degree plays a universal role in cooperation occurring on all these networks, that is the density of cooperators peaks at some specific values of the average degree. Moreover, we investigated the average payoff of players through numerical simulations together with theoretical predictions and found that simulation results agree with the predictions. Our work may be helpful in understanding network effects on the evolutionary games.     

Elimination mechanism promotes cooperation in coevolutionary prisoner’s dilemma games

We propose an elimination mechanism in the study of the evolutionary prisoner’s dilemma games on evolving networks. It assumes that after each round of playing, players whose payoffs are below a certain threshold will be eliminated from the game and the same number of new nodes will be added to the network to maintain the size of the network constant. Numerical results show that moderate values of elimination threshold can result in a maximum cooperation level in the evolutionary prisoner’s dilemma game. Moreover, the elimination mechanism can make the network structure evolve into a high heterogeneity in degree distribution, which is considered to be helpful in promoting cooperation in evolutionary games. The present study may provide new insight for understanding the evolution of cooperation in light of the law ‘survival of the fittest’ in nature.     

Negativity as Entanglement Degree of a Non-Hermitian Model

We investigate non-Hermitian Hamiltonian which governs system includes two-level atoms and electromagnetical field. Using the notion of negativity, we study the degree of entanglement of a two- level atom interacting with a quantized electromagnetical field, described by the non-Hermitian Hamiltonian (Saaidi in Phys. Scr. 77:0065002, 2008). With the help of numerical calculation for the case that the system state is pure, we show that the measurement of negativity of this system is nonzero and has a different functional with respect to negativity of the Jaynes-Cumming model (JCM).     

Modulation of Entanglement for Coupled Superconducting Qubits Under Non-Markovian Environment

The evolution of entanglement decoherence is investigated for a coupled superconducting qubit under non-Markovian environment by utilizing a commensal entanglement degree. The results show that, owing to the memory feedback effect of environment, the entanglement degree of the coupled qubits at the thermal equilibrium always monotonously tends to zero so that entanglement sudden death occurs briefly in the non-Markovian process. Different from the Markovian process, stronger the dissipation is, faster the entanglement sudden death is. We find that, furthermore, the interaction between the qubits results generally in reduction of entanglement degree in the quantum system. With some special initial states or initial phase angles, however, the influence of the interaction between qubits on the system entanglement degree can be avoided.     

Experimental realization of quantum games on a quantum computer

We generalize the quantum prisoner's dilemma to the case where the players share a nonmaximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region, and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.     

Entanglement Dynamics and Transfer for Two-Qubit Werner-Like States in Markovian Environments

We investigate entanglement dynamics and transfer in a system of two identical independent qubits, each of them locally interacting with a bosonic reservoir. Starting from two-qubit extended Werner-like states, we have shown that the degree of entanglement of the initial states, Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs’ entanglement sudden birth. Moreover, the phenomenon of entanglement sudden death/birth may occur depending on the values of parameters like purity or degree of entanglement of the initial state. When initial states are not pure, entanglement sudden death/birth always occurs, this will permit us to link the occurrence time of entanglement sudden death/birth and entanglement transfer to the purity or the degree of entanglement of the initial states.     

Transmissions of quantum entangled states in anisotropic depolarizing channels

We investigate the effect of an anisotropic depolarizing channel on the classical transmission of quantum entangled states. We calculate numerically mutual information between honest parts as a function of the degree of anisotropy of the depolarizing channel. In contrast to the case of isotropic channels, we found that the mutual information depends on both the degree of anisotropy and the degree of entanglement. It increases with increase in the degree of entanglement for a quantum channel with sufficiently large depolarizing anisotropy and decreases with increase in the entanglement.