diff --git a/povm_toolbox/library/dilation_measurement.py b/povm_toolbox/library/dilation_measurement.py
index 4aa22e7..b0f1b4a 100644
--- a/povm_toolbox/library/dilation_measurement.py
+++ b/povm_toolbox/library/dilation_measurement.py
@@ -22,7 +22,7 @@
     from typing import override  # pragma: no cover
 
 import numpy as np
-from qiskit.circuit import ClassicalRegister, QuantumCircuit, QuantumRegister
+from qiskit.circuit import AncillaRegister, ClassicalRegister, QuantumCircuit, QuantumRegister
 from qiskit.primitives.containers import DataBin
 from qiskit.primitives.containers.bindings_array import BindingsArray
 from qiskit.primitives.containers.bit_array import BitArray
@@ -168,13 +168,15 @@ def _build_qc(self) -> QuantumCircuit:
         t1 = time.time()
         LOGGER.info("Building POVM circuit")
 
-        qr = QuantumRegister(2 * self.num_qubits, name="povm_qr")
+        qr = QuantumRegister(self.num_qubits, name="povm_qr")
+        ar = AncillaRegister(self.num_qubits, name="povm_ancillas")
         cr = ClassicalRegister(2 * self.num_qubits, name=self.classical_register_name)
-        qc = QuantumCircuit(qr, cr, name="measurement_circuit")
+        qc = QuantumCircuit(qr, ar, cr, name="measurement_circuit")
         for i in range(self.num_qubits):
             qc.unitary(self._unitary_from_parameters(self._parameters[i]), [i, i + self.num_qubits])
 
-        qc.measure(qr, cr)
+        qc.measure(qr, cr[: self.num_qubits])
+        qc.measure(ar, cr[self.num_qubits :])
 
         t2 = time.time()
         LOGGER.info(f"Finished circuit construction. Took {t2 - t1:.6f}s")
diff --git a/povm_toolbox/library/product_povm_implementation.py b/povm_toolbox/library/product_povm_implementation.py
new file mode 100644
index 0000000..da6fd3c
--- /dev/null
+++ b/povm_toolbox/library/product_povm_implementation.py
@@ -0,0 +1,134 @@
+# (C) Copyright IBM 2024.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""MixedPOVMImplementation."""
+
+from __future__ import annotations
+
+import logging
+import sys
+import time
+
+if sys.version_info < (3, 12):
+    pass
+else:
+    pass  # pragma: no cover
+
+from qiskit.circuit import (
+    AncillaRegister,
+    QuantumCircuit,
+)
+from qiskit.primitives.containers import DataBin
+from qiskit.primitives.containers.bindings_array import BindingsArray
+from qiskit.primitives.containers.bit_array import BitArray
+from qiskit.primitives.containers.sampler_pub import SamplerPub
+from qiskit.transpiler import StagedPassManager
+
+from povm_toolbox.quantum_info import ProductPOVM
+
+from .metadata import POVMMetadata
+from .povm_implementation import POVMImplementation
+
+LOGGER = logging.getLogger(__name__)
+
+
+class MixedPOVMImplementation(POVMImplementation[POVMMetadata]):
+    """TODO."""
+
+    def __init__(
+        self,
+        num_qubits: int,
+        sub_implementations: list[POVMImplementation],
+        *,
+        insert_barriers: bool = False,
+    ) -> None:
+        """Initialize TODO POVM.
+
+        Args:
+            num_qubits: the number of qubits.
+            sub_implementations: TODO.
+            insert_barriers: whether to insert a barrier between the composed circuits. This is not
+                done by default but can prove useful when visualizing the composed circuit.
+
+        Raises:
+            ValueError: TODO.
+        """
+        super().__init__(num_qubits, measurement_layout=None, insert_barriers=insert_barriers)
+
+        self._sub_implementations = sub_implementations
+
+        check_num_qubits = 0
+        for i, sub_implementation in enumerate(self._sub_implementations):
+            sub_implementation.classical_register_name += f"_{i}"
+            sub_implementation.measurement_circuit = sub_implementation._build_qc()
+            check_num_qubits += sub_implementation.num_qubits
+
+        if self.num_qubits != check_num_qubits:
+            raise ValueError()
+
+        # NOTE: this public attribute inherits its docstring from the base class
+        self.measurement_circuit = self._build_qc()
+
+    def _build_qc(self) -> QuantumCircuit:
+        """Build the quantum circuit that implements the measurement.
+
+        Returns:
+            TODO.
+        """
+        t1 = time.time()
+        LOGGER.info("Building POVM circuit")
+        qc = QuantumCircuit(self.num_qubits)
+        n = 0
+        for sub_implementation in self._sub_implementations:
+            qc.add_register(*sub_implementation.measurement_circuit.cregs)
+            index_layout = []
+            for qreg in sub_implementation.measurement_circuit.qregs:
+                if isinstance(qreg, AncillaRegister):
+                    index_layout += list(range(qc.num_qubits, qc.num_qubits + len(qreg)))
+                    qc.add_register(qreg)
+                else:
+                    index_layout += list(range(n, n + len(qreg)))
+                    n += len(qreg)
+            qc = qc.compose(
+                sub_implementation.measurement_circuit,
+                qubits=index_layout,
+                clbits=sub_implementation.measurement_circuit.clbits,
+            )
+
+        t2 = time.time()
+        LOGGER.info(f"Finished circuit construction. Took {t2 - t1:.6f}s")
+
+        return qc
+
+    def definition(self) -> ProductPOVM:
+        """Return the corresponding quantum-informational POVM representation."""
+        return
+
+    def to_sampler_pub(
+        self,
+        circuit: QuantumCircuit,
+        circuit_binding: BindingsArray,
+        shots: int,
+        *,
+        pass_manager: StagedPassManager | None = None,
+    ) -> tuple[SamplerPub, POVMMetadata]:
+        return
+
+    def reshape_data_bin(self, data: DataBin) -> DataBin:
+        return
+
+    def _povm_outcomes(
+        self,
+        bit_array: BitArray,
+        povm_metadata: POVMMetadata,
+        *,
+        loc: int | tuple[int, ...] | None = None,
+    ) -> list[tuple[int, ...]]:
+        return