Determining a quantum state in a subspace with a single apparatus

We suggest a protocol for determining an unknown quantum state in a subspace using a single apparatus within an enlarged Hilbert space. This constitutes a positive operator valued measurement (POVM) scheme, where the large Hilbert space comes from a direct sum of a complementary subspace and the system's subspace, rather than from the conventional direct product of the Hilbert space of an ancilla (a subsystem) with that of the system. We propose an experimental implementation using a multi-level atom interacting with laser fields.