# Quantum Structure for Modelling Emotion Space of Robots
## 1 Introduction  
Emotional intelligence is primarily concerned with the capacity of an entity (human or robot) to exhibit, control, and express emotions and the ability to handle interpersonal (i.e., human-human, human-robot, or robot-robot) relationships judiciously and empathetically. Accomplishing this entails discerning between different emotions, labelling them appropriately, using them to guide thinking and behaviour, as well as managing and/or adjusting emotions to adapt to changes in environment, situations, and scenarios [1]. The intrigues required to model such multi-variate and continuously-changing feelings make descriptions of emotional state and their often-wovering transition from one state to another a very daunting exercise. To mimic the uncertainty related to emotions and their transitions, the notion of emotion space is used. An emotion space is used to quantitatively and visually imitate a human or robot's emotions as it interacts with itself, others, and its environment over some interval in time [2]. Our review of the timeline for use of emotion space in emotional intelligence kicks off with [PERSON] from 1997, wherein a pleasure-arousal (PA) judgement space was proposed as a psychological judgement space for assessing affective feelings [3]. In that study, two dimensions were associated with the general characteristics needed to represent both the specific emotion as well as their continuous variation. Therefore, each emotion could be placed in the resulting PA space when emotion-eliciting factors are translated into appropriate values in the coordinate system. In 2001, a three-dimensional space was used to define as a mental model for a robot based on the PA space [4]. A certainty axis, which is a continuously varying value in the range \(-1\) to +1, was added to this new space to produce smooth and effective communication between humans and robots. Subsequently, considering the rapid variation in mental state due to real-time human-robot interaction, an affinity-pleasure-arousal space was proposed in [2]. In this model, the affinity axis was used to describe the transition from one mental state to another as dictated by the progress in the conversation and repetitive interaction. The pleasure-displeasure and arousal-sleep axes in the space are related to the happiness of interlocutor as well as the liveliness in the dialogue, respectively. In 2013, [PERSON] et al. proposed the concept of fuzzy atmosfield (FA) to represent the atmosphere created during interactive communication involving many humans and/or roots [5]. This study employed a 3D fuzzy cubic space to represent the sates of the FA where the three coordinates are defined as \"Friendly-Hostile\", \"Lively-Calm\", and \"Casual-Formal\" within the range \(-1\) to +1. Most of the available representations and discussions on emotion space in the literature [6; 7] are formulated using conventional arithmetic, relying purely on the use of mathematical expressions and computation. The uncertainty, instantaneous and infinitesimal nature of emotions and their transitions suggest that a more rigorous and superior framework is required to efficiently decipher emotional intelligence. Exploiting the overwhelming superiority that quantum information processing offers [8], the potential to realise more powerful and efficient operations were explored. In [9], [PERSON] et al. provided a quantum mechanical model of robot-specific emotions based on quantum cellular automata. To facilitate this, they described a robot as a set of functional agents, each acting on behalf of its own emotional function; hence, generating the whole robot emotional state. Years later, [PERSON] et al. proposed the concepts that apply quantum circuits to model fuzzy sets, thereby creating a new method to model emotional behaviors for a humanoid robot [10]. This new method makes use of the entanglement and partial measurement properties from quantum mechanics available to the modeling of fuzzy systems to evolve behaviours of humanoid robots with a genetic algorithm [11].