Asymmetric quantum decision-making.

Collective decision-making plays a crucial role in information and communication systems. However, decision conflicts among agents often impede the maximization of potential utilities within the system. Quantum processes have shown promise in achieving conflict-free joint decisions between two agents through the entanglement of photons or the quantum interference of orbital angular momentum (OAM). Nonetheless, previous studies have shown symmetric resultant joint decisions, which, while preserving equality, fail to address disparities. In light of global challenges such as ethics and equity, it is imperative for decision-making systems to not only maintain existing equality but also address and resolve disparities. In this study, we investigate asymmetric collective decision-making theoretically and numerically using quantum interference of photons carrying OAM or entangled photons. We successfully demonstrate the realization of asymmetry; however, it should be noted that a certain degree of photon loss is inevitable in the proposed models. We also provide an analytical formulation for determining the available range of asymmetry and describe a method for obtaining the desired degree of asymmetry.

Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference.

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.

Entangled and correlated photon mixed strategy for social decision making.

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.

Entangled N-photon states for fair and optimal social decision making.

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N-player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.

Entangled-photon decision maker.

The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. The study described herein provides experimental evidence that entangled photons physically resolve the CMAB in the 2-arms 2-players case, maximizing the social rewards while ensuring equality. Moreover, we demonstrated that deception, or outperforming the other player by receiving a greater reward, cannot be accomplished in a polarization-entangled-photon-based system, while deception is achievable in systems based on classical polarization-correlated photons with fixed polarizations. Besides, random polarization-correlated photons have been studied numerically and shown to ensure equality between players and deception prevention as well, although the CMAB maximum performance is reduced as compared with entangled photon experiments. Autonomous alignment schemes for polarization bases were also experimentally demonstrated based only on decision conflict information observed by an individual without communications between players. This study paves a way for collective decision making in uncertain dynamically changing environments based on entangled quantum states, a crucial step toward utilizing quantum systems for intelligent functionalities.

Plasmonic core-shell nanostructure as an optical photoactive nanolens for enhanced light harvesting and hydrogen production.

Hydrogen production using plasmonic photocatalyst has attracted increasing attention since it improves light harvesting and photoefficiency. Herein, we have designed a plasmonic photocatalyst in a core-shell nanostructure that enabled an improvement of light harvesting and photocatalytic production of hydrogen using a very low amount of gold nanoparticles. The core-shell nanostructure was found to mimic the focusing of light observed for the lens-like epidermal cells. Thus, the core-shell nanostructure acts as a convex nanolens to reinforce the electromagnetic field at the nanostructure surface. The electric field was also found to be enhanced, which improves the energy absorbed for gold particles located in the core-shell nanostructure. Thus, by adjusting the diameter of the core-shell nanostructure, an optimal intensity for the localized surface plasmon resonance of gold was obtained. Tuning the size of the core-shell nanostructure enabled to improve the absorption at the reactive surface, thus increasing the photocatalytic hydrogen production efficiency by 5-fold.

Silencing and enhancement of second-harmonic generation in optical gap antennas.

Amplifying local electromagnetic fields by engineering optical interactions between individual constituents of an optical antenna is considered fundamental for efficient nonlinear wavelength conversion in nanometer-scale devices. In contrast to this general statement we show that high field enhancement does not necessarily lead to an optimized nonlinear activity. In particular, we demonstrate that second-harmonic responses generated at strongly interacting optical gap antennas can be significantly suppressed. Numerical simulations are confirming silencing of second-harmonic in these coupled systems despite the existence of local field amplification. We then propose a simple approach to restore and amplify the second-harmonic signal by changing the manner in which electrically-connected optical antennas are interacting in the charge-transfer plasmon regime. Our observations provide critical design rules for realizing optimal structures that are essential for a broad variety of nonlinear surface-enhanced characterizations and for realizing the next generation of electrically-driven optical antennas.

Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation.

We report the three-dimensional mapping of 150 nm gold metallic nanoparticles dispersed in a homogeneous transparent polyacrylamide matrix using second-harmonic generation. We demonstrate that the position of single nanoparticles can be well defined using only one incident fundamental beam and the harmonic photon detection performed at right angle. The fundamental laser beam properties are determined using its spatial autocorrelation function and used to prove that single nanoparticles are observed. Polarization resolved measurements are also performed allowing for a clear separation of the second-harmonic response of the single gold metallic nanoparticles from that of aggregates of such nanoparticles.

Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium.

We report the optical second harmonic generation from individual 150 nm diameter gold nanoparticles dispersed in gelatin. The quadratic hyperpolarizability of the particles is determined and the input polarization dependence of the second harmonic intensity obtained. These results are found in excellent agreement with ensemble measurements and finite element simulations. These results open up new perspectives for the investigation of the nonlinear optical properties of noble metal nanoparticles.

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique.

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.