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 ΔCr and the uncertainty ΔCq 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 $$ {\left(\Delta A\right)}^2{\left(\Delta B\right)}^2>{\left|\frac{1}{2}\left\langle \right[A,B\left]\right\rangle \right|}^2 $$ . From such inequality we impose bounds for both uncertainties Δξr and Δξq.