The relationship between quantum and classical correlation in games

It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both fundamental and practical importance. In consideration of the unavoidable interaction between correlated systems and the environment, understanding the dynamics of correlations would stimulate great interest. In this study, we investigate the dynamics of different kinds of bipartite correlations in an all-optical experimental setup. The sudden change in behaviour in the decay rates of correlations and their immunity against certain decoherences are shown. Moreover, quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation. Our observations may be important for quantum information processing.

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.

Freezing of quantum and classical correlations via trace and Hellinger distances

Environment and initial state engineered dynamics of quantum and classical correlations

The property of quantum correlation has been studied in recent years, especially for the quantum and classical correlations affected by environment. The dynamics of quantum and classical correlations in two-qubit system under identical local noise channels have been investigated recently. Here we will consider the dynamics of quantum and classical correlations when the local noise channels of two sides are not identical. We investigate the dynamics of quantum and classical correlations with three types of local noise channels in both Markovian and non-Markovian conditions, and show the decay rules of quantum and classical correlations with different types and parameter times of local noise channels.

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

This article presents a unified probabilistic framework that allows both rational and irrational decision-making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of game-theoretic models, which assumes that a decision-maker chooses the best action according to their preferences. In this article, we define irrationality as a deviation from a rational choice. Bistable probabilities are proposed as a principled and straightforward means for modelling (ir)rational decision-making in games. Bistable variants of classical and quantum Prisoner's Dilemma, Stag Hunt and Chicken are analysed in order to assess the effect of (ir)rationality on agent utility and Nash equilibria. It was found that up to three Nash equilibria exist for all three classical bistable games and maximal utility was attained when agents were rational. Up to three Nash equilibria exist for all three quantum bistable games; however, utility was shown to increase according to higher levels of agent irrationality.

Several different definitions of quantum games have been proposed over the past five years. Some of the results claimed for the differences between these quantum games and classical games identified as those to which they correspond have been criticized, however, as not being fair comparisons. In this paper I define classical and quantum versions of games with mediated communication, and propose that these are the classical and quantum games that should be compared.

Classical and quantum correlations for two-mode coherent-state superposition

Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

The second quantum revolution is all about exploiting the quantum nature of atoms and molecules to execute quantum information processing tasks. To boost this growing endeavor and by anticipating the key role of quantum chemistry therein, our work establishes a framework for systematically exploring, quantifying and dissecting correlation effects in molecules. By utilizing the geometric picture of quantum states we compare—on a unified basis and in an operationally meaningful way—total, quantum and classical correlation and entanglement in molecular ground states. To unlock and maximize the quantum informational resourcefulness of molecules an orbital optimization scheme is developed, leading to a paradigm-shifting insight: a single covalent bond equates to the entanglement . This novel and more versatile perspective on electronic structure suggests a generalization of valence bond theory, overcoming deficiencies of modern chemical bonding theories.

We show that for two initially excited qubits, interacting via dipole forces and with a common reservoir, entanglement is preceded by the emergence of quantum and classical correlations. After a time lag, entanglement finally starts building up, giving rise to a peculiar entangled state, with very small classical correlations. Different measures of quantum correlations are discussed, and their dynamics are compared and shown to lead to coincident values of these quantifiers for several ranges of time.

Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord, and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, whereas total, classical, and entanglement correlations can reduce the work extraction.

Quantum correlations from classically correlated states

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.