Single-Shot Quantum Process Tomography

Abstract: The standard procedure for quantum process tomography (QPT) involves applying the quantum process on a system initialized in each of a complete set of orthonormal states. The corresponding outputs are then characterized by quantum state tomography (QST), which itself requires the measurement of non-commuting observables realized by independent experiments on identically prepared system states. Thus QPT procedure demands a number of independent measurements, and moreover, this number increases rapidly with the size of the system. However, the total number of independent measurements can be greatly reduced with the availability of ancilla qubits. Ancilla assisted process tomography (AAPT) has earlier been shown to require a single QST of system-ancilla space. Ancilla assisted quantum state tomography (AAQST) has also been shown to perform QST in a single measurement. Here we combine AAPT with AAQST to realize a `single-shot QPT' (SSPT), a procedure to characterize a general quantum process in a single collective measurement of a set of commuting observables. We demonstrate experimental SSPT by characterizing several single-qubit processes using a three-qubit NMR quantum register. Furthermore, using the SSPT procedure we experimentally characterize the twirling process and compare the results with theory.