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

• Published in: Annalen der Physik Vol. 534; no. 5
• Main Authors: Lu, Guo‐Dong, Zhang, Zhou, Dai, Yue, Dong, Yu‐Li, Zhang, Cheng‐Jie
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.05.2022
• Subjects: ancilla‐assisted quantum process tomography; bound entangled states; Entangled states; entanglement detection; Realignment; Tomography
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.202100550

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. It is shown that entanglement is not necessary for ancilla‐assisted quantum process tomography. Surprisingly, by presenting two examples of two‐qutrit entangled states, it is found that there also exist some entangled states that are useless for ancilla‐assisted quantum process tomography. Moreover, experimental verification is also performed on the IBM platform.