Work

Certifying Entanglement Dimensionality by k -Reduction Moments

Year: 2025

Type: article

Abstract: In this paper, we combine the k -reduction map, the moment method, and randomized measurements into a practical protocol for certifying the entanglement dimensionality. Our approach is based on the observation that a state with entanglement dimensionality at most k must stay positive under the action of the k -reduction map. The core of our protocol utilizes the moment method to determine whether the k -reduced operator, i.e., the operator obtained after applying the k -reduction map on a quantum state, contains a negative eigenvalue or not. Notably, we propose a systematic method for constructing reduction moment criteria that apply to a broader range of states, including k -unfaithful states, compared with fidelity-based methods. The performance of our approach gets better and better with the moment order employed, which is corroborated by extensive numerical simulations. To apply our approach, it suffices to implement a unitary 3-design instead of a 4-design, which is more feasible in practice than the correlation matrix method. In the course of study, we show that the k -reduction negativity, the absolute sum of the negative eigenvalues of the k -reduced operator, is monotonic under local operations and classical communication for pure states.

Source: PRX Quantum

DOI: 10.1103/cc1n-gmj1

Authors: Changhao Yi, Xiaodi Li, Huangjun Zhu

Institutions: Shanghai University, Fudan University, State Key Laboratory of Surface Physics, Shanghai Research Center for Quantum Sciences, IFlyTek (China)

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China