Uncertainty Inequality for the Entanglement of Both Two-rebits and Two-qubits States

Abstract

We assume that both the concurrence Cr of a two-rebits state and the concurrence Cq of the usual two-qubits states are represented by hermitian operators (observables). We calculate the respective uncertainty Cr and the uncertainty Cq measured both as the standard deviation . We make the strictly mathematical assumption that there exists a canonical conjugate variable (called ξ ) to the concurrence (C) such that both quantities satisfy a Robertson’s [1] uncertainty inequality of the form (A)2(B)2 > | 1 2 [A, B]|2. From such inequality we impose bounds for both uncertainties ξ r and ξ q.