We present a web-based interactive music system that generates sound through the framework of twoplayer quantum game theory. Two users connect via a internet browser interface, select quantum strategies, and trigger notes by pressing piano keys. Each input initiates a two-qubit circuit whose measurement probabilistically collapses into one of four outcomes, each linked to a payoff pair inspired by the Prisoner’s Dilemma. These sampled payoffs determine pitch shifts relative to a neutral baseline, producing distinct sounds for each player.The system provides real-time visual and auditory feedback, allowing participants to perceive how their own strategies intertwine with those of their opponent through quantum interference and measurement. Beyond applications in music and education, the framework also models improvisatory interplay-akin to jazz performance-where each player’s decision reshapes the shared horizon of possible outcomes. This platform opens new avenues for exploring quantum games, human-computer interaction, and entangled decision-making through sound.
We present a web-based interactive music system that generates sound through the framework of twoplayer quantum game theory. Two users connect via a internet browser interface, select quantum strategies, and trigger notes by pressing piano keys. Each input initiates a two-qubit circuit whose measurement probabilistically collapses into one of four outcomes, each linked to a payoff pair inspired by the Prisoner’s Dilemma. These sampled payoffs determine pitch shifts relative to a neutral baseline, producing distinct sounds for each player.The system provides real-time visual and auditory feedback, allowing participants to perceive how their own strategies intertwine with those of their opponent through quantum interference and measurement. Beyond applications in music and education, the framework also models improvisatory interplay-akin to jazz performance-where each player’s decision reshapes the shared horizon of possible outcomes. This platform opens new avenues for exploring quantum games, human-computer interaction, and entangled decision-making through sound.
Decision-making by the two negotiating parties is simulated by a prisoner's dilemma game.The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options.Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state.The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized.On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair.We show that quantum prisoner's dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions.Some economical examples of utilizing quantum game Nash equilibria are proposed.
This paper introduces an interactive music system with quantum musical agents that communicate by teleporting quantum states to one another. Human performers interact in real time with agents whose melodic and rhythmic behaviours are encoded as quantum states using Single Qubit Probability Amplitude Modulation (SQPAM) and structured through Quantum Phase Estimation (QPE). Up to three agents are combined within a single quantum circuit, with directed communication via quantum teleportation. We are interested in supporting ambiguous, transformative interactions reminiscent of free Jazz improvisation. Therefore, rather than treating noise and decoherence as limitations, the system embraces NISQ-era constraints as creative affordances, framing agent communication as quantum whispers, that is, deliberate, musically expressive imperfections in state transfer. We provide demonstrations and analyses based on melodic correlation, pitch-set distance, and state fidelity, where a continuum between imitation and divergence can be observed. We developed a tunable interpretation method to assess how agents reinterpret teleported states. This work positions teleportation as a promising interaction mechanism for agent-based quantum computer music and outlines future directions toward distributed ensembles connected via the Quantum Internet.
Abstract We present a time-dependent quantum game-theoretic framework to analyze general two-voice contrapuntal structures. Utilizing the polyphony of J.S. Bach as a representative proof of concept, we model the functional interdependence of independent voices using a multi-contextual binary abstraction of tonal harmony. By incorporating an entanglement parameter and a payoff penalty reflecting asymmetric musical roles, we extract underlying quantum strategies from symbolic musical data. Our optimization demonstrates that the game-theoretic model assuming quantum entanglement reproduces empirical probability distributions with significantly higher accuracy than the corresponding unentangled baseline model. Furthermore, applying the payoff penalty drives the system beyond classical limits, revealing that the structural demands of counterpoint actively exploit nonlocal quantum correlations. Finally, we show that the resulting payoff-induced probabilistic deviations can be mathematically mapped to temporal timing fluctuations. This exploratory study provides a physics-based foundation for interpreting structurally driven deviations from a musical score as emergent temporal dynamics in creative performance.
We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2times2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well known quantum games, the Battle of Sexes and the Chicken game.
This work is mainly based on quantum game-theoretic techniques and their application to quantum information theory.Quantum game theory is an important development in quantum computation and may have implications for quantum information and quantum communication.The select of quantum memory on quantum games have been studied.Three dierent games such as, Prisoner Dilemma, Battle of the Sexes and Chicken have been analyzed in the quantum domain. By considering the restricted game \nsituation, it is shown that the ects of quantum memory and decoherence become eective in a maximally entangled case.For which the quantum player can out perform the classical player in all the three games. It is also shown that the quantum player enjoys an advantage over the classical player in Battle of the Sexes game for the amplitude-damping and the depolarizing channels.The quantum memory compensates the reduction in player pay is due to decoherence. It has no ect on the Nash equilibria of the three games.A generalization of two-player quantization scheme to a three-player Prisoners Dilemma game under the ect of correlated noise is also presented.In a restricted game scenario, it is shown the quantumplayer is always better; for all values of the decoherence parameter for the entire range of memory parameter.It is seen that for maximum degree of correlation, the game does not become \nnoiseless and quantum player can still outscore the classical players for the entire range of the decoherence parameter producing an interesting result in comparison with a two-player quantum game.It is also shown that correlated noise has not on the Nash equilibrium of the game.By exploiting the three-player quantization scheme, we have studiedthe communication aspects of a three-player Prisoner Dilemma quantum game. It is shown that entanglement plays a dominant role in a three-player quantum game.On the baois of initial state and the measurement basis entanglement parameters, a relation among different pay is established.It is investigated that the strategies of the players act as information carriers in quantum games. A relationship for the information shared among the parties is also established.A scheme for quantum key distribution is proposed in which a secret key can be generated from the data coming through a partially entanglement breaking channel.This scheme is rather deterministic andcient in the sense that two classical bits can be transferred \nper entangled pair of qubits.Furthermore, it is important to point out that, in this scheme, same symbol can be used for Eve detection and key generation. It is also worth noting that the eavesdropper, Eve, can be detected very easily from the disturbance of the elements of the decoding bimatrix. We have checked for the \nsecurity of the scheme and found it secure against individual attacks.It is further investigated that quantum games are useful in developing quantum cryptographic protocols.A multiparty quantum cryptographic protocol using tripartite entangled GHZ states is devised using game-theoretic techniques.In this protocol, two classical bits can be transferred per entangled pair of qubits to the communicating parties.Unitary operators applied by the sender on a tripartite entangled state encodes a classical symbol that can be decoded at receiver end with the help of a decoding matrix. In this protocol, if Eve interferes during the transmission, she can be detected by the disturbance of the decoding matrix. Our security analysis shows that this protocol is also secure against intercept/re-send attacks.
Purpose The current paper is a brief review of the emerging field of quantum-like modelling in game theory. This paper aims to explore several quantum games, which are superior compared to their classical counterparts, which means either they give rise to superior Nash equilibria or they make the game fairer. For example, quantum Prisoners Dilemma generates Pareto superior outcomes as compared to defection outcome in the famous classical case. Again, a quantum-like version of cards game can make the game fairer, increasing the chance of winning of players who are disadvantaged in the classical case. This paper explores all the virtues of simple quantum games, also highlighting some findings of the authors as regards Prisoners Dilemma game. Design/methodology/approach As this is a general review paper, the authors have not demonstrated any specific mathematical method, rather explored the well-known quantum probability framework, used for designing quantum games. They have a short appendix which explores basic structure of Hilbert space representation of human decision-making. Findings Along with the review of the extant literature, the authors have also highlighted some new findings for quantum Prisoners Dilemma game. Specifically, they have shown in the earlier studies (which are referred to here) that a pure quantum entanglement set up is not needed for designing better games, even a weaker condition, which is classical entanglement is sufficient for producing Pareto improved outcomes. Research limitations/implications Theoretical research, with findings and implications for future game designs, it has been argued that it is not always needed to have true quantum entanglement for superior Nash Equilibria. Originality/value The main purpose here is to raise awareness mainly in the social science community about the possible applications of quantum-like game theory paradigm. The findings related to Prisoners Dilemma game are, however, original.