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

TL;DR

This paper presents simple algorithms for generating multi-term Bell-like bases using novel controlled-unitary gates, revealing diverse entanglement properties and highlighting monogamy score as a key quantum correlation measure.

Contribution

It introduces new controlled-unitary gates and algorithms that unify and extend previous methods for constructing entangled Bell-like bases, with analysis of their quantum correlations.

Findings

Bell-like bases are superpositions of 2^m terms with equal amplitudes.

Different controlled-unitaries produce bases with varying entanglement.

Monogamy score effectively distinguishes quantum correlations among bases.

Abstract

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.