Clifford operators play a vital role in quantum computation and information. Conventionally, a single-qudit Clifford operator maps the complete set of generalized Pauli matrices (GPMs) onto itself under conjugation. However, many practical quantum information tasks—such as local discrimination of generalized Bell states (GBSs)—only require mapping a specific subset of GPMs to another, rather than the entire set. To address this we introduce the concept of a local Clifford operator, defined as a unitary operator that conjugates a given set of $n$ GPMs into another such set. We establish necessary and sufficient conditions for such an operator to transform a pair of GPMs and show that these operators admit a generalized symplectic representation, analogous to the symplectic representation of standard Clifford operators. Furthermore, we give a generalized symplectic representation of any local Clifford operator acting on an $n$-GPM set. The generalized symplectic representation of local Clifford operators is directly applicable to determining the local unitary equivalence of sets of GBSs—a fundamental problem in quantum information, with applications in tasks such as local state discrimination. Our results thus bridge algebraic structures and physical applications, offering new tools for classifying and manipulating quantum states and operations.

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• Nonlocality
• Quantum entanglement