Not All Entangled States are Useful for Ancilla-Assisted Quantum Process Tomography

It is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum-process tomography and ancilla-assisted quantum process tomography (AAQPT). Furthermore, it is shown that entanglement is not necessary for AAQPT; there exist separable states that are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT; there also exist some entangled states that are useless. The realignment operation used in entanglement detection can be related to the question whether a bipartite state is useful for AAQPT. The relationship between them is derived and the process of extracting the complete information of an unknown channel by the realignment operation shown. Based on this relationship, examples of a two-qutrit entangled state and a two-qutrit bound entangled state are presented. Both of these two examples are entangled but they cannot be used for AAQPT. Last but not the least, experimental verification is been performed on the IBM platform.

Automated summary

This article investigates the applicability of entangled states in quantum process tomography and finds that not all entangled states are suitable for ancilla-assisted quantum process tomography (AAQPT). The relationship between the realignment operation used in entanglement detection and the usefulness of a bipartite state for AAQPT is derived. Examples of entangled states that cannot be used for AAQPT are presented. Experimental verification is performed on the IBM platform.