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29 March 2024
 
  » arxiv » 1601.5379

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Pure State Tomography with Pauli Measurements
Xian Ma ; Tyler Jackson ; Hui Zhou ; Jianxin Chen ; Dawei Lu ; Michael D. Mazurek ; Kent A. G. Fisher ; Xinhua Peng ; David Kribs ; Kevin J. Resch ; Zhengfeng Ji ; Bei Zeng ; Raymond Laflamme ;
Date 20 Jan 2016
AbstractWe examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary $n$-qubit pure state among all quantum states. We show that only $11$ Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with $16$ measurements, and only $31$ Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with $64$ measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.
Source arXiv, 1601.5379
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