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arXiv · 1511.00581

Tomography is necessary for universal entanglement detection with single-copy observables

Dawei Lu·Tao Xin·Nengkun Yu·Zhengfeng Ji·Jianxin Chen·Guilu Long·Jonathan Baugh·Xinhua Peng·Bei Zeng·Raymond Laflamme
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Abstract

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the $k$-symmetric extendibility.

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Dawei Lu, Tao Xin, Nengkun Yu, Zhengfeng Ji, Jianxin Chen, Guilu Long, Jonathan Baugh, Xinhua Peng, Bei Zeng, Raymond Laflamme. 2015-11-02. Tomography is necessary for universal entanglement detection with single-copy observables. https://doi.org/10.1103/physrevlett.116.230501

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