Search Results (7)

The concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner’s Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. The resulting Nash equilibria are found to be more closely aligned with Pareto-optimal solutions than those of the conventional Nash equilibrium outcome of the classical game. Our results demonstrate the complexity and diversity of strategic behavior in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In particular, we provide a detailed characterization of strategy profiles and their corresponding Nash equilibria, thereby extending the understanding of quantum strategies’ impact on traditional game-theoretical problems. Full article

With the rapid advances in quantum computing, quantum security is now an indispensable property for any cryptographic system. In this paper, we study how to prove the security of a complex cryptographic system in the quantum random oracle model. We first give a variant of Zhandry’s compressed random oracle (CStO), called a compressed quantum random oracle with adaptive special points (CStO_s). Then, we extend the on-line extraction technique of Don et al. (EUROCRYPT’22) from CStO to ${\mathbf{CStO}}_s$. We also extend the random experiment technique of Liu and Zhandry (CRYPTO’19) for extracting the $\mathbf{CStO}$ query that witnesses the future adversarial output. With these preparations, a systematic security proof in the quantum random oracle model can start with a random CStO experiment (that extracts the witness for the future adversarial output) and then converts this game to one involving ${\mathbf{CStO}}_s$. Next, the online extraction technique for ${\mathbf{CStO}}_s$ can be applied to extract the witness for any online commitment. With this strategy, we give a security proof of our recent compact multi-signature framework that is converted from any weakly secure linear ID scheme. We also prove the quantum security of our recent lattice realization of this linear ID scheme by iteratively applying the weakly collapsing protocol technique of Liu and Zhandry (CRYPTO 2019). Combining these two results, we obtain the first quantum security proof for a compact multi-signature. Full article

A quantum game is constructed from a sequence of independent and identically polarised spin-1/2 particles. Information about their possible polarisation is provided to a bettor, who can wager in successive double-or-nothing games on measurement outcomes. The choice at each stage is how much to bet and in which direction to measure the individual particles. The portfolio’s growth rate rises as the measurements are progressively adjusted in response to the accumulated information. Wealth is amassed through astute betting. The optimal classical strategy is called the Kelly criterion and plays a fundamental role in portfolio theory and consequently quantitative finance. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy. This paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm. Intriguing trade-offs between information gain and portfolio growth are described. Full article

The aim of the paper is to examine pure Nash equilibria in a quantum game that extends the classical bimatrix game of dimension 2. The strategies of quantum players are specific types of two-parameter unitary operations such that the resulting quantum game is invariant under isomorphic transformations of the input classical game. We formulate general statements for the existence and form of Nash equilibria and discuss their Pareto efficiency. We prove that, depending on the payoffs of a classical game, the corresponding quantum game may or may not have Nash equilibria in the set of unitary strategies under study. Some of the equilibria cease to be equilibria if the players’ strategy set is the three-parameter special unitary group. Full article

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states. Full article

As humanity grapples with the concept of autonomy for human–machine teams (A-HMTs), unresolved is the necessity for the control of autonomy that instills trust. For non-autonomous systems in states with a high degree of certainty, rational approaches exist to solve, model or control stable interactions; e.g., game theory, scale-free network theory, multi-agent systems, drone swarms. As an example, guided by artificial intelligence (AI, including machine learning, ML) or by human operators, swarms of drones have made spectacular gains in applications too numerous to list (e.g., crop management; mapping, surveillance and fire-fighting systems; weapon systems). But under states of uncertainty or where conflict exists, rational models fail, exactly where interdependence theory thrives. Large, coupled physical or information systems can also experience synergism or dysergism from interdependence. Synergistically, the best human teams are not only highly interdependent, but they also exploit interdependence to reduce uncertainty, the focus of this work-in-progress and roadmap. We have long argued that interdependence is fundamental to human autonomy in teams. But for A-HMTs, no mathematics exists to build from rational theory or social science for their design nor safe or effective operation, a severe weakness. Compared to the rational and traditional social theory, we hope to advance interdependence theory first by mapping similarities between quantum theory and our prior findings; e.g., to maintain interdependence, we previously established that boundaries reduce dysergic effects to allow teams to function (akin to blocking interference to prevent quantum decoherence). Second, we extend our prior findings with case studies to predict with interdependence theory that as uncertainty increases in non-factorable situations for humans, the duality in two-sided beliefs serves debaters who explore alternatives with tradeoffs in the search for the best path going forward. Third, applied to autonomous teams, we conclude that a machine in an A-HMT must be able to express itself to its human teammates in causal language however imperfectly. Full article

Braid’s (Jonathan Blow, 2008) time-bending gameplay allows players to engage with a virtual world in which a player’s perceived ‘past’ can be endlessly rewritten, duration extended, and the ludic arrow of time can be reversed. One could assume that as mistakes can simply be undone, in-game actions cease to have consequences. However, the climax of the game’s narrative arc disrupts our assumption of control over these mechanics and encourages players to reflect on the possible moral implications of actions, both in context of the game world and—through careful invocation of real-world scientific experiments—on everyday life. In this paper, I propose that Braid uses gameplay to explore the difficulty of making moral judgements in a world without an objective past. This is, for the most part, achieved through Braid’s utilization of a specific interpretation of quantum theory—in accordance with the game’s lead designer, Jonathan Blow—that “starts to threaten our very existence” by questioning the possibility of a singular, objective, real ‘past’ and the possibility of a definitive account of past actions. I first argue that the game’s mechanics immerse players in a game world inspired by Blow’s understanding of quantum mechanics. Placing an emphasis on certain technical aspects, I outline how the functioning of the game’s central rewind mechanic—although initially seeming to reinforce visions of our reality consistent with C.D. Broad’s ‘growing block’ theory—questions the notion of an objective past and so resonates strongly with both the work of J.A. Wheeler and an agential realist theory of time. With this understanding in place, I go on to analyze the climax of the game, reading it as an exploration of—and challenge to—the role of a presumed objective ‘past’ in understanding the morality of a given situation. Finally, through a reading of the game’s closing moments, I suggest Braid promotes a turn to individual responsibility for agency; Braid, I argue, recommends one accept the continuing existence and changeability of the past within the present while embracing one’s own role in the shared process of constantly remaking reality and history. As a result, well-intentioned actions in the present are framed as more important than a focus on precedent to predict outcomes, making a cautious suggestion on how one might live without reference to an objective existence. Although I highlight some of the wider ramifications of this at the end of this paper, Braid is far from a fully developed ethical system; it stands, however, as an engaging attempt to formulate a comment on time, temporality and morality through interactive media. Full article