Dynamical quantum state tomography with time-dependent channels

• URL: http://arxiv.org/abs/2402.05431v1
• Date: Thu, 8 Feb 2024 06:02:00 GMT
• Title: Dynamical quantum state tomography with time-dependent channels
• Authors: Meng Cao and Yu Wang
• Abstract summary: We establish a dynamical quantum state tomography framework. Under certain condition, it is possible to obtain infinite families of projective operators. We show how to simulate a SIC-POVM on any unknown quantum state.
• Score: 31.94084207707832
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we establish a dynamical quantum state tomography framework. Under this framework, it is feasible to obtain complete knowledge of any unknown state of a $d$-level system via only an arbitrary operator of certain types of IC-POVMs in dimension $d$. We show that under the time-dependent average channel, we can acquire a collection of projective operators that is informationally complete (IC) and thus obtain the corresponding IC-POVMs. We show that under certain condition, it is possible to obtain infinite families of projective operators that are IC, and obtain infinite families of corresponding IC-POVMs; otherwise, the Zauner's conjecture is incorrect. We also show how to simulate a SIC-POVM on any unknown quantum state by using the time-dependent average channel.

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