Higher Dimension Quantum Entanglement Generators

Abstract

Quantum information processing and communication techniques rely heavily upon entangled quantum states, and this dependence motivates the development of methods and systems to generate entanglement. Much research has been dedicated to state preparation for radix-2 qubits, and due to the pursuit of entangled states, the Bell state generator and its generalized forms where the number of entangled qubits is greater than two have been defined. In this work, we move beyond radix-2 and propose techniques for quantum state entanglement in high-dimensional systems through the generalization of the binary bipartite entanglement states. These higher-radix quantum informatic systems are composed of n quantum digits, or qudits, that are each mathematically characterized as elements of an r -dimensioned Hilbert vector space where r > 2. Consequently, the wave function is a time-dependent state vector of dimension r n . The generalization of the binary controlled-NOT to the controlled-modulo-addition gate, the concept of partial versus maximal entanglement, and architectures for generating higher-radix entangled states for the partial and maximal case are all presented.