[work in progress] Clarify "conjugate" method purpose

qiskit/circuit/library/generalized_gates/unitary.py

@@ -123,7 +123,7 @@ def inverse(self, annotated: bool = False):
         return self.adjoint()
 
     def conjugate(self):
-        """Return the conjugate of the unitary."""
+        """Return the complex conjugate of the unitary with respect to the representation returned by ``to_matrix``."""
         return UnitaryGate(numpy.conj(self.to_matrix()))
 
     def adjoint(self):

qiskit/quantum_info/operators/mixins/adjoint.py

@@ -45,7 +45,7 @@ def adjoint(self) -> Self:
 
     @abstractmethod
     def conjugate(self) -> Self:
-        """Return the conjugate of the CLASS."""
+        """Return the complex conjugate of the CLASS."""
 
     @abstractmethod
     def transpose(self) -> Self:

qiskit/quantum_info/operators/symplectic/pauli_list.py

@@ -810,7 +810,7 @@ def _multiply(self, other):
         return PauliList(super()._multiply(other))
 
     def conjugate(self):
-        """Return the conjugate of each Pauli in the list."""
+        """Return the complex conjugate of each Pauli in the list with respect to the Z basis."""
         return PauliList(super().conjugate())
 
     def transpose(self):

qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py

@@ -291,6 +291,7 @@ def __setitem__(self, key, value):
     # ---------------------------------------------------------------------
 
     def conjugate(self):
+        """Return the complex conjugate with respect to the representation returned by ``to_matrix``."""
         # Conjugation conjugates phases and also Y.conj() = -Y
         # Hence we need to multiply conjugated coeffs by -1
         # for rows with an odd number of Y terms.

qiskit/quantum_info/states/densitymatrix.py

@@ -210,7 +210,7 @@ def to_operator(self) -> Operator:
         return Operator(self.data, input_dims=dims, output_dims=dims)
 
     def conjugate(self):
-        """Return the conjugate of the density matrix."""
+        """Return the complex conjugate of the density matrix."""
         return DensityMatrix(np.conj(self.data), dims=self.dims())
 
     def trace(self):

qiskit/quantum_info/states/stabilizerstate.py

@@ -189,7 +189,8 @@ def to_operator(self) -> Operator:
         return Clifford(self.clifford).to_operator()
 
     def conjugate(self):
-        """Return the conjugate of the operator."""
+        """Return the complex conjugate of the underlying Clifford operator with
+        respect to the representation returned by the operator's ``to_matrix`` method."""
         ret = self.copy()
         ret._data = ret._data.conjugate()
         return ret

qiskit/quantum_info/states/statevector.py

@@ -246,7 +246,7 @@ def to_operator(self) -> Operator:
         return Operator(mat, input_dims=self.dims(), output_dims=self.dims())
 
     def conjugate(self) -> Statevector:
-        """Return the conjugate of the operator."""
+        """Return the complex conjugate of the state vector."""
         return Statevector(np.conj(self.data), dims=self.dims())
 
     def trace(self) -> np.float64: