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Entanglement as Internal Constraint

Diederik Aerts·Ellie D'Hondt·Bart D'Hooghe
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Abstract

Our investigation aims to study the specific role played by entanglement in the quantum computation process, by elaborating an entangled spin model developed within the 'hidden measurement approach' to quantum mechanics. We show that an arbitrary tensor product state for the entity consisting of two entangled qubits can be described in a complete way by a specific internal constraint between the ray and density states of the two qubits. For the individual qubits we use a sphere model representation, which is a generalization of the Bloch or Pauli representation, where also the collapse and noncollapse measurements are represented. We identify a parameter r in [0,1], arising from the Schmidt diagonal decomposition, that is a measure of the amount of entanglement, such that for r = 0 the system is in the singlet state with 'maximal' entanglement, and for r = 1 the system is in a pure product state.

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Diederik Aerts, Ellie D'Hondt, Bart D'Hooghe. 2002-10-04. Entanglement as Internal Constraint. https://arxiv.org/abs/quant-ph/0210035

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