Not all entangled states are useful for ancilla-assisted quantum process tomography

TL;DR

This paper investigates the conditions under which entangled states are useful for ancilla-assisted quantum process tomography, revealing that not all entangled states are beneficial, supported by theoretical analysis and experimental verification.

Contribution

It establishes that some entangled states are not useful for AAQPT and links entanglement detection via realignment to the usefulness for process tomography.

Findings

Some entangled states are useless for AAQPT.

Realignment operation relates to the usefulness of states for AAQPT.

Experimental verification confirms theoretical predictions.

Abstract

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 has been shown that entanglement is not necessary for AAQPT, there exist separable states which 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 which are useless. The realignment operation used in entanglement detection can be related to the question whether a bipartite state is useful for AAQPT. We derive the relationship between them and show the process of extracting the complete information of an unknown channel by the realignment operation. Based on this relationship, we present examples of a two-qutrit entangled state and a two-qutrit bound entangled state. Both of these two examples are entangled but they cannot be used for AAQPT. Last but not least, experimental verification has also been performed on the IBM platform.