O produto de quartebits não gera um qubit entrelaçado

Abstract

The quaterbit is the smallest unit of information of Quaternion quantum mechanics. Their study brings to light fundamental problems of Quantum Mechanics that also have implications in Information Theory and Quantum Computation. In this work, it was investigated whether a pair of quaterbits may be entangled in Quantum Mechanics of complex numbers. To verify this hypothesis, two arbitrary quaterbits were used as singlets and we did the tensorial product. From this tensorial product, we establish the necessary conditions for the state to be only in Complex Quantum Mechanics. Within this procedure, two particular cases were analyzed: pure state and a simple case of mixed state. For pure states, we nd that the resulting separable bipartite qubit is not entangled, and therefore we conclude that the tensor product of two pure quaterbits does not result in a bipartite pure qubit entangled. Finally, we consider a mixed state of disentangled quaterbits (with some restrictions) and establish the conditions so that it lies only in Complex Quantum Mechanics, and therefore we conclude by using the Wootters concurrence that the state is disentangled.