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A recursive approach to determine the Hilbert-Schmidt measure of pairwisequantum discord in a special class of symmetric states of $k$ qubits ispresented. We especially focus on the reduced states of $k$ qubits obtainedfrom a balanced superposition of symmetric $n$-qubit states (multiqubitSchr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots,n-1)$. Two pairing schemes are considered. In the first one, the geometricdiscord measuring the correlation between one qubit and the party grouping$(k-1)$ qubits is explicitly derived. This uses recursive relations between theFano-Bloch correlation matrices associated with subsystems comprising $k$,$k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, threeand four qubit systems. In the second scheme, the subsystem comprising the$(k-1)$ qubits is mapped into a system of two logical qubits. We show thatthese two bipartition schemes are equivalents in evaluating the pairwisecorrelation in multi-qubits systems. The explicit expressions of classicalstates presenting zero discord are derived.

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states