# Quantum Structure for Modelling Emotion Space of Robots
## 1 Introduction
These works are treated as the pioneering results in quantum emotion studies, although, neither of them provides a specific mathematical formulation to describe the quantum emotion and its space. In [12], [PERSON] et al. formulated a quantum Bloch sphere-based representation for emotion space, where two angles \(\phi\) and \(\theta\) in the Bloch sphere were used to represent the emotions of robots and its intensity (or strength), respectively. However, since emotion and intensity were stored in a superposition state, the study could not offer a concrete information retrieval protocol to recover the available information about the robot's emotion(s). In this study, we propose a reformulated emotion space but as a prelude to that, we pause to ponder over two questions: (1) what are the quantum mechanical properties that could support effective expression of emotion? and (2) how does this \"quantumness\" relate to the description of a quantum robot (or qubot)? While there are others, answering these two questions as well as exploring the integration of some of the remarkable advances recorded in quantum image processing [13; 14] to descriptions of emotion space and emotional intelligence provide few of the motivations for this study. Now, we proceed to answer the questions posed earlier. First, employing quantum mechanics to describe emotion space presupposes the potential use of lower computing resources (since quantum parallelism offers exponential speed up relative to the required number of qubits as well as the sufficient (polynomial) number of CNOT gates that are needed to manipulate a quantum emotion, which sharply decreases the computational complexity of the process) and also quantum mechanics ensures that all transformations are unitary and reversible, so that the robot's emotion could be easily transferred (forward or backward) within the emotion space. Regarding the second question that was posed earlier, by envisioning a qubot as a mobile quantum system that includes an on-board quantum computer and its required anciliary systems [15], it is reasonable to imagine that qubits will carry out tasks whose goals include specified changes in conformity with the state of the environment or even carrying out measurements on the environment itself [16; 17]. Moreover, it is envisioned that future robots will operate in all kinds of environments: manipulating, controlling, and interacting with different sensors, which themselves capture massive amounts of data. Furthermore, the invigorated interest in and funding for quantum computation suggests that the quantum era is upon us [18] and inevitably quantum hardware will play one role or the other in future robot communication be it as standalone units or as part of larger sophisticated hybrid systems. In tandem with these projections, presently, quantum technologies have been employed to improve the capability of conventional computing tasks by assuming their coalescence as peripherals of other sophisticated classical computing hardware [19]. Similarly, integrating quantum mechanics into descriptions of emotion space supports the development of qubits as well as its use to manipulate classical robot devices to perform advanced emotion-related actions [20]. The first step in exploiting the superlative properties of quantum computation in robotics is formulating its representation within the precepts of quantum mechanics. Consequent upon the foregoing, in this study, we propose a layout to depict the quantum emotion space (QES) by utilising three entangled qubit sequences to locate an emotion point within a three-dimensional emotion space. From this, two qubit sequences will be allocated to elicit the type of emotion, while the remaining sequence will be dedicated for ascertaining the temporal information related to each emotion. In QES, a robot's quantum emotion at each instance is a unique point in an emotion space, whereas the trajectory of a time interval produces a curve that depicts changes in the emotion with time.