01598nas a2200241 4500008004100000245005800041210005800099260001500157300001100172490000800183520093100191100001301122700001401135700001801149700001601167700001801183700001801201700001301219700001601232700001401248700002201262856007201284 2017 eng d00aQuantum state tomography via reduced density matrices0 aQuantum state tomography via reduced density matrices c2017/01/09 a0204010 v1183 a
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.
1 aXin, Tao1 aLu, Dawei1 aKlassen, Joel1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aMa, Xian1 aLong, Guilu1 aZeng, Bei1 aLaflamme, Raymond uhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.02040101933nas a2200277 4500008004100000245007200041210006900113260001500182300001100197490000700208520116900215100001301384700001901397700001401416700001801430700001401448700002501462700002301487700001701510700001701527700002101544700001801565700001401583700002201597856003601619 2016 eng d00aPure-state tomography with the expectation value of Pauli operators0 aPurestate tomography with the expectation value of Pauli operato c2016/03/31 a0321400 v933 aWe 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.
1 aMa, Xian1 aJackson, Tyler1 aZhou, Hui1 aChen, Jianxin1 aLu, Dawei1 aMazurek, Michael, D.1 aFisher, Kent, A.G.1 aPeng, Xinhua1 aKribs, David1 aResch, Kevin, J.1 aJi, Zhengfeng1 aZeng, Bei1 aLaflamme, Raymond uhttp://arxiv.org/abs/1601.0537901747nas a2200241 4500008004100000245009400041210006900135260001500204300001100219490000800230520106300238100001401301700001301315700001601328700001801344700001801362700001601380700002001396700001701416700001401433700002201447856003601469 2016 eng d00aTomography is necessary for universal entanglement detection with single-copy observables0 aTomography is necessary for universal entanglement detection wit c2016/06/07 a2305010 v1163 aEntanglement, 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.1 aLu, Dawei1 aXin, Tao1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aLong, Guilu1 aBaugh, Jonathan1 aPeng, Xinhua1 aZeng, Bei1 aLaflamme, Raymond uhttp://arxiv.org/abs/1511.0058102052nas a2200193 4500008004100000245002200041210002200063260001300085300001200098490000800110520156800118100002301686700001901709700002201728700002301750700002401773700002401797856003701821 2010 eng d00aQuantum Computing0 aQuantum Computing c2010/3/4 a45 - 530 v4643 a Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. 1 aLadd, Thaddeus, D.1 aJelezko, Fedor1 aLaflamme, Raymond1 aNakamura, Yasunobu1 aMonroe, Christopher1 aO'Brien, Jeremy, L. uhttp://arxiv.org/abs/1009.2267v1