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29 March 2024 |
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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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