We investigate the validity of quantum Fisher information (QFI) as a helpful coherence quantifier by drawing a comparison with first-order coherence (FOC) and some other relevant quantifiers to study the coherence and correlations in the quasi-Werner entangled coherent states (quasi-WECS). We identify QFI as a more useful coherence quantifier as it quantifies coherences of individual subsystems and correlations between them. On the other hand, FOC identifies coherences present in the individual subsystems only. Our results show that all of these coherence quantifiers follow the same behavior toward their maximum (or minimum) values for experimentally achievable values of the mean photon number.

We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.

We calculate the quantum capacity of an amplitude-damping channel with time-correlated Markov noise, for two channel uses. Our results show that memory of the channel increases its ability to transmit quantum information significantly. An upper bound on the amount of quantum information transmitted over the channel in the presence of memory, for an arbitrary number of channel uses, is also presented.

We calculate the information capacities of a time-correlated amplitude-damping channel, provided the sender and receiver share prior entanglement. Our analytical results show that the noisy channel with zero capacity can transmit information if it has finite memory. The capacities increase as the memory increases attaining maximum value for perfect memory channel.

We have studied an early stage disentanglement by solving an exactly solvable spin bath model in the Markovian and non-Markovian regimes. In the Markovian regime, the central two qubit spins are non-interacting in which entanglement strongly depends on mean number of photon. In the non-Markovian regime, we solved by considering and ignoring the interaction between central two spins and observe that the entanglement strongly depends on the spin bath interaction, qubit spin interaction, bath spin interaction, thermal temperature and the initial state. Further, the concurrence of an initially unentangled state mixed with an entangled state also depends on the initial state.

We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.

We quantize the Hawk–Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed evolutionarily stable strategies (ESS). An example is considered to draw a comparison between the classical and quantum version of the game. Our choice of the most general initial quantum state enables us to make the game symmetric or asymmetric. We show that for a particular set of game parameters where there exists only mixed ESS in the classical version of the game, quantization allows even a pure strategy to be an ESS for the symmetric game in addition to mixed ESS. On the other hand only pure strategy ESS can exist for the asymmetric quantum version of the Hawk–Dove game.

We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.

We have proposed a generalized quantuzation secheme for non-zero sum games which can be reduced to two existing quantization schemes under appropriate set of parameters. Some other importnat situations are identified which are not apparent in the exiting two quantizations schemes.

We analyze quantum game with correlated noise through generalized quantization scheme. Four different combinations on the basis of entanglement of initial quantum state and the measurement basis are analyzed. It is shown that the advantage that a quantum player can get by exploiting quantum strategies is only valid when both the initial quantum state and the measurement basis are in entangled form. Furthermore, it is shown that for maximum correlation the effects of decoherence diminish and it behaves as a noiseless game.

An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamic but not every attractor is an ESS. We search for a dynamic characterization of ESSs in quantum games and find that in certain asymmetric bi-matrix games evolutionary stability of attractors can change as the game switches between its two forms, one classical and other quantum.

We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory i.e. an Evolutionarily Stable Strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.

We analyzed quantum version of the game Battle of Sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the Battle of Sexes can be resolved and a unique solution of the game can be obtained.

We find quantum mechanics playing a role in evolutionary dynamics described by the notion of an Evolutionarily Stable Strategy (ESS). An ESS being a refinement of Nash equilibrium concept is a stable strategy in an evolutionary game with replicator dynamic as the underlying process. We investigate ESSs in two and three player symmetric quantum games played by the proposed scheme of applying ′ identity ′ and ′ Pauli spin-flip ′ operators on an initial state, in its originally proposed simpler form, with classical probabilities. The mixed Nash equilibrium (NE) we search for is not affected by a switch-over between two forms of the game, one quan-tized and other classical. However it is an ESS when the game is played classically. We show no such mixed NE exists for two player games in the originally proposed scheme with its particular entangled initial state but there is a class of three player games where they do exist. Our results imply that an evolutionary approach originating with Darwin's idea of natural selection can be used even in quantum setting indicating the possibility of evolutionary algorithms utilizing entanglement and other quantum effects.

We find the requirements on change of evolutionary stability of a mixed Nash equilibrium (NE) when a game changes its form from classical to quantum or conversely. We consider a quantized two players two strategies symmetric game. We find that an entangled state in a more general form is needed to affect evolutionary stability of a mixed NE than needed, with similar purpose, for a pure NE.

We investigate the extension of the concept of Evolutionary Stable Strategies (ESS's) to quantum domain. We show that for the pair-wise game of Prisoner's Dilemma played in a population a two-parameter quantum strategy can invade a classical ESS. However in this game a quantum ESS cannot be invaded by another two parameter quantum strategy. Game theory has been successfully applied in mod-eling the evolutionary processses in natural world. Certain paradoxical situations[1,2] in animal conflicts have been explained by the game theory. The concept of an Evolutionary Stable Strategy (ESS) was introduced by Maynard Smith and Price [3]. An ESS is a strategy, which if adopted in a conflict by a population ,can withstand a small invading group. The ESS is thus stable and persists through time, provided that the payoff matrix and available strategies remain unchanged. The concept of an ESS developed from applying the ideas of game theory to animal conflicts and recently certain ideas of game theory have been extended to quantum domain [4,5]. The generalization into quantum domain of certain games has already been considered [4]. If the genes engage themselves in selfish games [6] played at molecular level where quantum mechanics decides the rules then it is interesting to speculate about the quantum analogues of ESS's. If the games of survival between animals give rise to ESS's then what about the possibility of quantum games among the molecules giving rise to quantum strategies that are stable and persist through time. If such a Quantum Evolutionary Stable Strategy (QESS) is a possibility then it may have interesting characteristics like its classical counterpart possess. They may be immune from invasion from other mutant quantum strategies. We consider the question of mutant quantum strategy trying to invade other classical or quantum ESS in a population engaged in a pair-wise game of Prisoner's Dilemma. We will consider the symmetric version of the pair-wise game where all members of the population are indistinguishable and each player is equally likely to meet any other player. In the Prisoner's Dilemma game the classical available pure strategies are Cooperation (C) and Defection (D) [7]. An interesting question is what strategies are likely to be stable and persistent in a population engaged in the pair-wise game of Prisoner's Dilemma. A simple analysis [8] show that D will be the pure classical strategy prevalent in the population. Suppose that a strategy A is played by almost …

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

We calculate the entanglement-assisted classical capacity of symmetric and asymmetric Pauli channels where two consecutive uses of the channels are correlated. It is evident from our study that in the presence of memory, a higher amount of classical information is transmitted over quantum channels if there exists prior entanglement as compared to product and entangled state coding.