Effectiveness of local unitary operations in $n$-local networks

Analyzing the nonclassicality of correlations generated in $n$-local quantum networks is an important branch of study in quantum information theory. Speaking of nonclassicality, violation of an $n$-local inequality ensures non $n$-locality of corresponding network correlations. Being correlation-based, violation of any such inequality is experimentally feasible. The present work explores whether applying suitable local unitary operations can aid violation of any $n$-local inequality. Observations have ensured the utility of local unitary operations in enhancing the detection efficiency of bilocal inequality and $n$-local inequality (for $n=3,4$) in the star configuration. In an $n$-local quantum network, such operations correspond to local basis change applied by at least one party over its joint state of qubits received from the sources. In an $n$-local network, with all the parties performing any possible local unitary operation, correlations not violating an $n$-local inequality (compatible with the network considered), are first characterized. Such characterization is then exploited to provide examples of local unitary operations aiding violation of existing $n$-local inequalities for $n=2$, 3, and 4, specifically. Interestingly, there exist two qubit unitary operations, for which nontrilocal correlations can be simulated even when one of the sources distribute pure product state in star network. Quantum gates associated with the useful unitary operations are provided.