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Algebraic approach to quantum non - separability is applied to the case oftwo qubits. It is based on the partition of the algebra of observables intoindependent subalgebras and the tensor product structure of the Hilbert spaceis not exploited. Even in this simple case, such general formulation has someadvantages. Using algebraic formalism we can explicitly show the relativity ofthe notion of entanglement to the observables measured in the system andcharacterize separable and non - separable pure states. As a universal measureof non - separability of pure states we propose to take so called totalcorrelation. This quantity depends on the state as well as on the algebraicpartition. Its numerical value is given by the norm of the correspondingcorrelation matrix

Entanglement beyond tensor product structure: algebraic aspects of quantum non - separability