Simple Algorithms for Multi-term Bell-like Bases and Their Quantum Correlations

We introduce two multiple qubit controlled-unitary gates with different working principles. We employ these gates and existing quantum gates to propose simple and efficient algorithms that generate multi-term orthonormal entangled Bell-like bases. All algorithms thus far known for constructing entangled bases turn out to be special cases of our method. The Bell-like states in any basis is superposition of $2^m$-terms with equal probabilities (that is, their amplitudes being $\pm 1/\sqrt{2^m}$). The orthogonality of the basis does not permit arbitrary amplitudes. The quantum correlations of these bases are investigated; we find that the Bell-like bases obtained using different controlled-unitaries have different entanglement contents. We also learn that monogamy score is able to distinguish these bases in the situations where other quantum correlations fail to do so indicating that monogamy score is a more fundamental quantum correlation measure. Our approach can be extended to qudit systems as well.