Asymmetric quantum decision-making

Abstract

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.

Figure 1

(a) The necessity of asymmetric treatments. The symmetric OAM system in the previous study can maintain the existing equality but cannot solve inequality. (b) Stochastic detection of OAM corresponds to a probabilistic selection of a player. Polarization enables us to diminish inequalities between players.

Figure 2

(a) System architecture for the asymmetric OAM decision making. It differs from the symmetric OAM system in that a PBS is added, and the basis of polarization is added to the photon state. PBS polarization beam splitter, BS beam splitter, SLM spatial light modulator, HW half wave plate. The zeroth-order extraction enables successful modulation with the SLM by extracting only the zeroth-order OAM from the initially generated light in a superposition of various OAMs. (b) Schematic illustration of the paths of photons.

Figure 3

Pairs of $(p_{12},p_{21})$ each system is able to realize. Blue dots are the results obtained by numerical experiments. Because blue dots exist outside the $p_{12}=p_{21}$ line, asymmetric decision-making is possible by all systems. (a) Asymmetric OAM system. (b) Entangled photon decision maker. (c) OAM attenuation.

Figure 4

The relationship between the loss probability plus conflict probability and the asymmetry ratio of each system. Blue dots are the results obtained by numerical experiments. The light blue area is the area mathematical consideration can prove that each system can realize. (a) Asymmetric OAM system. (b) Entangled photon decision maker. (c) OAM attenuation.

Figure 5

(a) The relationship between $\theta$ and r when $a_1=b_2=0$. (b) The relationship between $\theta$ and r when $a_2=b_1=0$. In both cases, any asymmetry ratio can be achieved by $\theta$, $-\pi /4\le \theta \le \pi /4$.

Figure 6

Experimental setup of the entangled photon decision maker. PBS polarization beam splitter, HW half-wave plate, APD avalanche photodiode, POLH polarizer (allowing only horizontal polarization to pass), POLV polarizer (allowing only vertical polarization to pass).

Figure 7

Decision-making system by OAM attenuation. HG hologram, ATT attenuator, BS beam splitter, SLM spatial light modulator.