Search Results (82)

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

We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and prey provides a well-justified and symmetric analysis. The main focus is placed on the Lagrange multiplier approach. Using natural physical units with Planck’s constant set to unity, it is recognized that energy has the dimensions of inverse time. Thus, the conjugate Lagrange multiplier, traditionally related to absolute temperature, is now taken with time units and oriented to follow the Arrow of Time. In quantum optics, where energy levels are bounded above and below, artificial singularities involving negative temperatures are eliminated. In a biological model where species compete in an environment with a fixed carrying capacity, use of the Canonical Ensemble solves an instance of Eigen’s phenomenological rate equations. The Lagrange multiplier emerges as a statistical measure of the ecological age. Adding a weak inequality on an order parameter for the entropy maximization, the phase transition from initial unconstrained growth to constrained growth at the carrying capacity is described, without recourse to a thermodynamic limit for the finite system. Full article

This paper explores the application of quantum game theory to optimize cloud resource allocation. By leveraging the principles of quantum mechanics, the proposed framework aims to enhance efficiency, reduce costs, and improve scalability in cloud computing environments. The study introduces a quantum-based game-theoretic model and compares its performance with classical approaches. The results demonstrate significant improvements in resource utilization and decision-making efficiency. While prior works have explored classical game theory and auction-based methods, this study is among the first to implement quantum game theory in a practical cloud computing context, propose a resource allocation mechanism that incorporates both fairness and efficiency while leveraging the computational advantages of quantum systems, and highlight the strategic benefits of quantum entanglement in fostering collaboration between competing entities in cloud environments. This work not only addresses the current limitations of resource allocation but also redefines the possibilities for optimization in complex systems, making a substantial contribution to both quantum computing and cloud resource management domains. Full article

The axiomatic framework of quantum game theory gives us a new platform for exploring economics by resolving the foundational problems that have long plagued the expected utility hypothesis. This platform gives us a previously unrecognized tool in economics, the statistical ensemble, which we apply across three distinct economic spheres. We examine choice under uncertainty and find that the Allais paradox disappears. For over seventy years, this paradox has acted as a barrier to investigating human choice by masking actual choice heuristics. We discover a powerful connection between the canonical ensemble and neoclassical economics and demonstrate this connection’s predictive capability by examining income distributions in the United States over 24 years. This model is an astonishingly accurate predictor of economic behavior, using just the income distribution and the total exergy input into the economy. Finally, we examine the ideas of equality of outcome versus equality of opportunity. We show how to formally consider equality of outcome as a Bose–Einstein condensate and how its achievement leads to a corresponding collapse in economic activity. We call this new platform ‘statistical economics’ due to its reliance on statistical ensembles. Full article

This paper introduces two information-theoretically quantum secure direct communication protocols that accomplish information exchange between Alice and Bob in the first case, and among Alice, Bob, and Charlie in the second case. Both protocols use a novel method, different from existing similar protocols, to embed the secret information in the entangled compound system. This new way of encoding the secret information is one of the main novelties of this paper, and a distinguishing feature compared to previous works in this field. A second critical advantage of our method is its scalability and extensibility because it can be seamlessly generalized to a setting involving three, or more, players, as demonstrated by the second protocol. This trait is extremely beneficial in many real-life situations, where many spatially separated players posses only part the secret information that must be transmitted to Alice, so that she may obtain the complete secret. Using the three-player protocol, this task can be achieved in one go, without the need to apply a typical QSDC protocol twice, where Alice first receives Bob’s and then Charlie’s information. The proposed protocol does not require pre-shared keys or quantum signatures, making it less complicated and more straightforward. Finally, in anticipation of the coming era of distributed quantum computing, our protocols offer the important practical advantage of straightforward implementation on contemporary quantum computers, as they only require standard CNOT and Hadamard gates. Full article

Feedback in group decision-making (GDM) is an effective procedure for eliminating preference inconsistencies among experts. As the core of GDM, feedback controls the progress and cost of the process. However, the current feedback model seldom considers interference effects caused by the interaction among experts. In addition, the stubbornness of experts to change preferences through interaction is different. This study proposes a bidirectional feedback model that considers interference effects. The model integrating quantum probability theory (QPT) into a feedback mechanism has greater flexibility and is more conducive to revealing modern cognitive psychology. First, experts were classified into concordant and stubborn discordant groups according to their personality parameters. Bidirectional feedback was proposed for a stubborn discordant group to improve the efficiency of feedback process and reduce the consensus-reaching cost. QPT was then used to describe the probability of experts modifying their preferences during the game process. Combining the interference value determined by the quantum probability with the feedback mechanism, a bidirectional feedback model driven by a minimum feedback control parameter is proposed to ensure that a certain consensus level can be achieved with minimal adjustment. The proposed feedback mechanism considers interference effects produced by experts in the interaction and can capture the feelings of conflict and compromise. Full article

In the context of multi-autonomous underwater vehicle (multi-AUV) operations, the target assignment is addressed as a multi-objective allocation (MOA) problem. The selection of strategy for multi-AUV target allocation is dependent on the current non-cooperative environment. This paper establishes a multi-AUV allocation situation advantage evaluation system to assess and quantify the non-cooperative environment. Based on this framework, a multi-AUV target allocation model using a bi-matrix game theory is developed, where multi-AUV target allocation strategies are considered as part of the strategic framework within the game. The payoff matrix is constructed based on factors including the situational context of multi-AUV operations, effectiveness, and AUV operational integrity. The Nash equilibrium derived from the game analysis serves as the optimal solution for resource distribution in multi-AUV non-cooperative scenarios. To address the challenge of finding the Nash equilibrium in bi-matrix games, this paper introduces a repulsion process quantum particle swarm optimization (RPQPSO) algorithm. This method not only resolves the complexities of Nash equilibrium computation but also overcomes the limitations of traditional optimization methods that often converge to local optima. A simulation experiment of multi-AUV operations is designed to validate the multi-AUV target allocation model, demonstrating that the RPQPSO algorithm performs effectively and is applicable to multi-AUV task scenarios. Full article

This paper presents a new quantum secret sharing scheme featuring a $(k,n)$ threshold and built-in verification. This innovative protocol takes advantage of entanglement and unfolds in three distinct phases. In anticipation of the coming of the distributed quantum computing era, this protocol is designed to function entirely in parallel within a fully distributed environment, where the spymaster and her agents are located in different places. This is a significant shift from most similar protocols that assume that all information recipients are in one location. The spymaster can send all necessary information to her agents at once, streamlining the process. Each phase runs simultaneously, which helps to reduce the overall execution cost. Given its complexity, we offer a thorough analysis to ensure its information-theoretic security, protecting against both external eavesdroppers and internal rogue agents. The protocol does away with the need for quantum signatures or pre-shared keys, making it simpler and less complex. Lastly, its potential for implementation on current quantum computers looks promising since it relies only on CNOT and Hadamard gates, with all participants using similar or identical quantum circuits. Full article

Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. Congestion of passengers, if considered as a network, may fall into the categories of optimization cases of quantum games. This paper explores the application of quantum potential games to minimize congestion in common areas at airports. The players/passengers of the airport have identical interests and they share the same utility function. A metric is introduced that considers a passenger’s visit to a common area by setting their preferences, in order to avoid congestion. Passengers can decide whether to visit a specific common area or choose an alternative. This study demonstrates that the proposed game is a quantum potential game for tackling congestion, with identical interests, ensuring the existence of a Nash equilibrium. We consider passengers to be players that want to ensure their interests. Quantum entanglement is utilized to validate the concept, and the results highlight the effectiveness of this approach. The objective is to ensure that not all passengers select the same common place of the airport to reduce getting crowded; hence, the airborne disease infection probability increases due to overcrowding. Our findings provide a promising framework for optimizing passenger flow and reducing congestion in airport common areas through quantum game theory. We showed that the proposed system is stable by encapsulating the Lyapunov stability. We compared it to a simulated annealing approach to show the efficacy of the quantum game approach. We acknowledge that this framework can be utilized in other disciplines as well. For our future work, we will research different strategies than binary ones to investigate the efficacy of the approach. 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

In this work, we present a new protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled $|GH{Z}_3⟩$ triplets. Our intention was to develop a protocol that can be readily executed by contemporary quantum computers. This is possible because the protocol uses only $|GH{Z}_3⟩$ triplets, irrespective of the number n of millionaires. Although it is feasible to prepare multiparticle entangled states of high complexity, this is overly demanding on a contemporary quantum apparatus, especially in situations involving multiple entities. By relying exclusively on $|GH{Z}_3⟩$ states, we avoid these drawbacks and take a decisive step toward the practical implementation of the protocol. An important quantitative characteristic of the protocol is that the required quantum resources are linear both in the number of millionaires and the amount of information to be compared. Additionally, our protocol is suitable for both parallel and sequential execution. Ideally, its execution is envisioned to take place in parallel. Nonetheless, it is also possible to be implemented sequentially if the quantum resources are insufficient. Notably, our protocol involves two third parties, as opposed to a single third party in the majority of similar protocols. Trent, commonly featured in previous multiparty protocols, is now accompanied by Sophia. This dual setup allows for the simultaneous processing of all n millionaires’ fortunes. The new protocol does not rely on a quantum signature scheme or pre-shared keys, reducing complexity and cost. Implementation wise, uniformity is ensured as all millionaires use similar private circuits composed of Hadamard and CNOT gates. Lastly, the protocol is information-theoretically secure, preventing outside parties from learning about fortunes or inside players from knowing each other’s secret numbers. Full article

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view. Full article

Process algebras have been developed within computer science and engineering to address complicated computational and manufacturing problems. The process algebra described herein was inspired by the Process Theory of Whitehead and the theory of combinatorial games, and it was developed to explicitly address issues particular to organisms, which exhibit generativity, becoming, emergence, transience, openness, contextuality, locality, and non-Kolmogorov probability as fundamental characteristics. These features are expressed by neurobehavioural regulatory systems, collective intelligence systems (social insect colonies), and quantum systems as well. The process algebra has been utilized to provide an ontological model of non-relativistic quantum mechanics with locally causal information flow. This paper provides a pedagical review of the mathematics of the process algebra. Full article

The expansion of underwater scenarios and missions highlights the crucial need for autonomous underwater vehicles (AUVs) to make informed decisions. Therefore, developing an efficient decision-making framework is vital to enhance productivity in executing complex tasks within tight time constraints. This paper delves into task planning and reconstruction within the AUV control decision system to enable intelligent completion of intricate underwater tasks. Behavior trees (BTs) offer a structured approach to organizing the switching structure of a hybrid dynamical system (HDS), originally introduced in the computer game programming community. In this research, an intelligent search algorithm, MCTS-QPSO (Monte Carlo tree search and quantum particle swarm optimization), is proposed to bolster the AUV’s capacity in planning complex task decision control systems. This algorithm tackles the issue of the time-consuming manual design of control systems by effectively integrating BTs. By assessing a predefined set of subtasks and actions in tandem with the complex task scenario, a reward function is formulated for MCTS to pinpoint the optimal subtree set. The QPSO algorithm is then leveraged for subtree integration, treating it as an optimal path search problem from the root node to the leaf node. This process optimizes the search subtree, thereby enhancing the robustness and security of the control architecture. To expedite search speed and algorithm convergence, this paper recommends reducing the search space by pre-grouping conditions and states within the behavior tree. The efficacy and superiority of the proposed algorithm are validated through security and timeliness evaluations of the BT, along with comparisons with other algorithms for automatic AUV decision control behavior tree design. Ultimately, the effectiveness and superiority of the proposed algorithm are corroborated through simulations on a multi-AUV complex task platform, showcasing its practical applicability and efficiency in real-world underwater scenarios. Full article

Quantum neural networks (QNNs) leverage the strengths of both quantum computing and neural networks, offering solutions to challenges that are often beyond the reach of traditional neural networks. QNNs are being used in areas such as computer games, function approximation, and big data processing. Moreover, quantum neural network algorithms are finding utility in social network modeling, associative memory systems, and automatic control mechanisms. Nevertheless, ensuring the reliability of quantum neural networks is crucial as it directly influences network performance and stability. To investigate the reliability of quantum neural networks, this paper proposes a methodology wherein operator measurements are performed on the final states of the output quantum states of a quantum neural network. The proximity of these measurements to the target value is compared, and the fidelity value, combined with a quantum gate operation, is utilized to assess the reliability of the quantum neural network. Through network training, the results demonstrate that, under optimal parameters, both the fidelity of the final state measurement value and the target value of the model approach are approximately equal to 1. It indicates that training mitigates the errors stemming from encoding into the initial quantum state, thereby resulting in enhanced system reliability and accuracy. Full article