Ancilla Assisted Quantum State Tomography in Many-Qubit Registers

The standard method of Quantum State Tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla Assisted QST (AAQST) proposed by Nieuwenhuizen and co-workers (Phys. Rev. Lett., 92, 120402 (2004)) greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. Here we describe methods for explicit construction of AAQST experiments in multi-qubit registers. We also report nuclear magnetic resonance studies on AAQST of (i) a two- qubit input register using a one-qubit ancilla in an isotropic liquid-state system and (ii) a three-qubit input register using a two-qubit ancilla register in a partially oriented system. The experimental results confirm the effectiveness of AAQST in such many-qubit registers.