QUANTUM ENTANGLEMENT ON A HYPERSPHERE

 

 

 

 

James F. Peters

Department of Electrical and Computer Engineering, University of Manitoba

75A Chancellor’s Circle

Winnipeg, MB R3T 5V6 CANADA

 

 

Arturo Tozzi (Corresponding Author)

Center for Nonlinear Science, University of North Texas

1155 Union Circle, #311427

Denton, TX 76203-5017 USA

 

International Journal of Theoretical Physics, 2016

DOI

10.1007/s10773-016-2998-7

 

 

 

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.   

 

 

YOU CAN FIND HERE A PREVIOUS VERSION OF THE PUBLISHED ARTICLE