Quantum Entanglement on a Hypersphere

Abstract

A quantum entanglement’s composite system does not display separable states and a single constituent cannot be fully described without considering the other states. We introduce quantum entanglement on a hypersphere - which is a 4D space undetectable by observers living in a 3D world -, derived from signals originating on the surface of an ordinary 3D sphere. From the far-flung branch of algebraic topology, the Borsuk-Ulam theorem states that, when a pair of opposite (antipodal) points on a hypersphere are projected onto the surface of 3D sphere, the projections have matching description. In touch with this theorem, we show that a separable state can be achieved for each of the entangled particles, just by embedding them in a higher dimensional space. We view quantum entanglement as the simultaneous activation of signals in a 3D space mapped into a hypersphere. By showing that the particles are entangled at the 3D level and un-entangled at the 4D hypersphere level, we achieved a composite system in which each local constituent is equipped with a pure state. We anticipate this new view of quantum entanglement leading to what are known as qubit information systems.