Limitations of Classically-Simulable Measurements for Quantum State Discrimination

Comparison between the quantum resource theory of magic states and entanglement.

Abstract

In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the computational resource theory. In this work, we investigate the limitations of classically-simulable measurements, specifically POVMs with positive discrete Wigner functions which include all stabilizer measurements, in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimension cannot be unambiguously distinguished by POVMs with positive discrete Wigner functions, regardless of how many copies of the states are supplied. We also give the asymptotic error probability for distinguishing the Strange state and its orthogonal complement. Moreover, we prove that every set of orthogonal pure stabilizer states can be unambiguously distinguished via POVMs with positive discrete Wigner functions, which is different from the existence of an unextendible product basis in entanglement theory. Our results reveal intrinsic similarities and distinctions between the quantum resource theory of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classicallysimulable measurements and contribute to a deeper understanding of the quantum-classical boundary.

Publication
arXiv:2310.11323
Chengkai Zhu
Chengkai Zhu
PhD Student

I obtained my BS in Applied Mathematics from China Agricultural University under the supervision of Prof. Zhencai Shen. I obtained my MS degree in Cyberspace Security from University of Chinese Academy of Sciences under the supervision of Prof. Zhenyu Huang. My research interests include quantum information theory and quantum computation.

Zhiping Liu
Zhiping Liu
Research Assistant

I obtained my BS in Physics from Nanjing University under the supervision of Prof. Jian Sun. I’m a PhD candidate of Quantum physics in Nanjing University under the supervision of Prof. Zengbing Chen. My research interests include quantum machine learning and quantum information theory.

Chenghong Zhu
Chenghong Zhu
PhD Student

I obtained my BS and MS degrees in computer science from the University of Melbourne. My research interests include distributed quantum computing, quantum entanglement and quantum machine learning.

Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.