Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

%B Physical Review Letters %V 118 %P 020401 %8 2017/01/09 %G eng %U http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401 %R 10.1103/PhysRevLett.118.020401 %0 Journal Article %J Physical Review A %D 2016 %T Pure-state tomography with the expectation value of Pauli operators %A Xian Ma %A Tyler Jackson %A Hui Zhou %A Jianxin Chen %A Dawei Lu %A Michael D. Mazurek %A Kent A.G. Fisher %A Xinhua Peng %A David Kribs %A Kevin J. Resch %A Zhengfeng Ji %A Bei Zeng %A Raymond Laflamme %XWe 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.

%B Physical Review A %V 93 %P 032140 %8 2016/03/31 %G eng %U http://arxiv.org/abs/1601.05379 %N 3 %R http://dx.doi.org/10.1103/PhysRevA.93.032140 %0 Journal Article %J Physical Review Letters %D 2016 %T Tomography is necessary for universal entanglement detection with single-copy observables %A Dawei Lu %A Tao Xin %A Nengkun Yu %A Zhengfeng Ji %A Jianxin Chen %A Guilu Long %A Jonathan Baugh %A Xinhua Peng %A Bei Zeng %A Raymond Laflamme %X 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. %B Physical Review Letters %V 116 %P 230501 %8 2016/06/07 %G eng %U http://arxiv.org/abs/1511.00581 %N 23 %R 10.1103/PhysRevLett.116.230501