A Geometrical Representation of Entanglement as Internal Constraint

Abstract

We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a 'rotation' and 'stretching' of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.Comment: 10 pages, 3 figures. submitted to International Journal of Theoretical Physic

Geometric analysis of entangled qubit pairs

“…Still, to some extent, geometric imagery is possible for a spin-1/2 state of a single electron which is customarily parametrized in terms of the Bloch or Poincaré sphere, where polar and azimuthal 2 angles can be interpreted as the Euler angles of a unity vector pointing along the spin direction. One possible generalization of the Bloch sphere is the sphere model, which gives a geometrical view of entanglement in terms of constraint functions describing the behaviour of the state of one of the spins if measurements are made on the other [8].…”

Compatibility and Separability for Classical and Quantum Entanglement

“…2) [6,7,8,9,20]. Also, the corresponding state transitions are the same, namely a collapse from the initial state towards an eigenstate of the observed outcome.…”

A Macroscopic Device for Quantum Computation

“…In general, in a 2-qubit quantum algorithm the register will be in other entangled states as well. In [7] we show how this problem is solved for the coupled sphere models by introducing constraint functions. Let us briefly recall how these functions are introduced and some of their properties.…”

“…This has lead to a 'quantum-like' sphere model which has a structure which is isomorphic to the spin structure for a spin 1/2 [5] and another system which entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state [6]. This model has been elaborated by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin [7]. This means that in principle one can represent any entangled state of a 2-qubit quantum computer with this model.…”