On Quantum Decision Trees

Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some properties of the states obtained in a decision tree structure. How these correlations may be mapped to the decision tree is considered. Classical tree representations and approximations to quantum states are provided. INTRODUCTION Imagine a decision system where the choices are made according to the measurements of a quantum state [1][2]. These choices may be mapped into a tree with each measurement is represented by a node (e.g. [3]). The node itself may be a human agent whose cognitions are modeled as a quantum system [4]-[7], or a classical agent that has access to quantum resources. Quantum models of cognition and information processing provide new insight into the workings of human agents in different decision environments (e.g. [8]-[11]) although it comes with features that do not have analogs in classical information [12][13]. Considerations under which quantum probability is the appropriate measure to use for cognitive processes have been examined from a variety of perspectives (e.g. [14]). In human agents, cognitive dissonance describes the stress arising out of holding two contradictory theories or ideas or actions [15][16]. The fact of such a state with contradictions is suggestive of superposition and thus it may justify the idea of quantum cognition. Quantum-like models have also been proposed to explain certain biological processes [17]. In engineered system the issue of dissonance is irrelevant and when considering quantum resources, mutually exclusive states will coexist. There is much research that has gone into measurements that can distinguish between classical and quantum states as evidenced by the great interest in hidden variable theories and the violation of Bell’s Inequalities [18][19]. The distinction between the two is on account of the fact that quantum states come with entanglement as a characteristic that shows up in nonlocality in physical processes and order effects in probability. The difference between classical and quantum domains can under certain conditions be ascertained by a condition on the ratios of the outcomes being the same (Ps) to being different (Pn) for 3-way coincidences. As shown earlier [20] for the classical and the maximally entangled quantum ( ) 11 00 ( 2 1    this ratio is given by: