Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum entanglement, which allows for quantum computations outperforming their classical counterparts. However, the task of entanglement detection is not always straightforward for several reasons. One of the main challenges is that standardly-used methods rapidly become unfeasible when dealing with quantum states containing more than a few qubits. Typically, this is due to the fact that a vast amount of measurements is needed on many copies of the state. Generally, it is not unusual to deal with a very limited number of state copies in experimental settings - in fact, this may be the case for many large quantum systems. In this article, an overview is provided of a probabilistic approach that enables high-confidence genuine multipartite entanglement detection using an exceptionally low number of state copies. Additionally, a study is presented that shows that this protocol remains efficient also in the presence of noise, thus confirming the practicality of the method for near-term quantum devices and its suitability for complex experimental settings.
We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved bette…
One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to achieve in practice when dealing with large-scale entangled quantum systems. In this letter we develop a novel method by formulating verification as a decision procedure, i.e. entanglement is seen as the ability of quantum system to answer certain "yes-no questions". We show that for a variety of large quantum states even a single copy suffices to detect entangle…
The phenomenon of quantum entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances trough photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn aroun…
Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most fundamental insights is the fact that some mixed states can feature entanglement across every possible cut of a multipartite system yet can be produced via a mixture of states separable with respect to different partitions. To distinguish states that genuinely cannot be produced from mixing such partition-separable states, the term genuine multipartite entanglement was coined. All these considerations originate in a paradigm where only a single cop…
Detecting entanglement of non-Gaussian continuous-variable states from single-copy homodyne measurements
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit（MajuLab，法国国家科学研究中心-尼斯大学-新加坡国立大学-南洋理工大学国际联合研究单位）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e.\ a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e.\ several copies of a biseparable state can display GME. We show that the set of GME-activatable stat…
A quantum state transformation can be generally approximated by single- and two-qubit gates. This, however, does not hold with noisy intermediate-scale quantum technologies due to the errors appearing in the gate operations, where errors of two-qubit gates such as controlled-NOT and SWAP operations are dominated. In this work, we present a cost efficient single-copy certification for a realization of a two-qubit gate in the presence of depolarization noise, where it is aimed to identify if the realization is noise-free, or not. It is shown that entangled resources such as entangled states and …
How best one can recycle a given quantum resource, mitigating the various difficulties involved in its preparation and preservation, is of considerable importance for ensuring efficient applications in quantum technology. Here we demonstrate quantitatively the resource theoretic advantage of reusing a single copy of a two-qubit entangled state towards information processing. To this end, we consider a scenario of sequential entanglement detection of a given two-qubit state by multiple independent observers on each of the two spatially separated wings. In particular, we consider equal numbers o…
Single-copy entanglement in a gapped quantum spin chain
定义了给定多体系统的单拷贝纠缠[J. J. J. Cramer，Phys. Rev. A. 72，042112（2005）]作为从该系统的单个样本的二分物确定性地可量化的最大纠缠。对于临界（无间隙）自旋链，最近的研究表明，这正好是冯诺伊曼熵的一半[R。Orus，J. I. Latorre，J. J. Cramer，Phys. Rev. A 73，060303（R）（2006）]，其本身被定义为在渐近极限中可纠缠的：即给定系统的无限数量的副本。对于带隙系统的等效行为是什么，这是一个悬而未决的问题。在本文中，我证明了对于典型的自旋-S-Affleck-Kennedy-Lieb-Tasaki链（原型带隙链），单拷贝纠缠等于冯诺伊曼熵：即所有存在的纠缠都可以从一个样本中提取出来.
Quantum technologies lead to a variety of applications that outperform their classical counterparts. In order to build a quantum device it must be verified that it operates below some error threshold. Recently, because of technological developments which allow for the experimental realization of quantum states with increasing complexity, these tasks must be applied to large multi-qubit states. However, due to the exponentially-increasing system size, tasks like quantum entanglement verification become hard to carry out in such cases. Here we develop a generic framework to translate any entangl…
Experimental Determination of Entanglement for Arbitrary Pure States
本文提出了一种实验上确定任意多体纯态局域观测量期望值的方法。在双量子比特系统的实验中，我们采用了对一个态的两个拷贝进行联合测量的方法[S。P. Walborn et al. Nature（London）440，20（2006）]，对于任意维的多体系统，我们在每次测量中只需要一个状态的副本，避免了准备孪生状态或状态的不完美副本。
Multi-photon entanglement has been successfully made by experimental groups. As the increase of photon number, several problems are encountered, say, greater number of copies, longer time, the error of fidelity and so on. In this paper, we present a new scheme based on Lagrange multiplier and feedback to save the measure copies in multi-photon experiment and five percent of measuring time, also guarantee the acceptable error of fidelity. All the results have been supported by the data of eight photon experiment. Furthermore, same approach is applied in the simulation for ten photon entanglemen…
Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We …
Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic meth…
Asymptotic quantification of entanglement with a single copy
Scuola Normale Superiore（高等师范学院）；QuSoft；Korteweg–de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学柯尔沃特-德弗里斯数学研究所）；Institute for Theoretical Physics, University of Amsterdam（阿姆斯特丹大学理论物理研究所）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Mathematical Quantum Information RIKEN Hakubi Research Team, RIKEN Pioneering Research Institute (PRI) and RIKEN Center for Quantum Computing (RQC)（理化学会Hakubi研究团队、理化学会先锋研究研究所及理化学会量子计算中心）
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different dimensions for single- and multi-copy regimes and establish a connection between state transformation and the difference between the entanglement contents of the initial and the target states. From the analysis of catalyst resources, required to further otherwise impossible LOCC transformations between pairs, we demonstrate a universal pattern in the average a…
Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state: \begin{align} \nonumber ρ_α= α\,|Φ^+ \rangle\langle Φ^+|+(1-α)\frac{\mathbb{1}}{4}. \end{align} We present two main results, consi…
Cryptography without Long-Term Quantum Memory and Global Entanglement: Classical Setups for One-Time Programs, Copy Protection, and Stateful Obfuscation
Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University（国立成功大学物理系与量子前沿研究与技术中心 (QFort)）
我们考虑了非正部分转置（NPT）束缚纠缠态的存在性问题。正如我们所知，这种状态的存在特别意味着可纠缠的不可加性。此外，它还排除了对一组可解释状态的简单数学描述。可蒸馏性等价于对于某个n的所谓的n拷贝可蒸馏性。我们考虑一个特定的状态，已知是1-副本不可分割的，这是应该是绑定纠缠。我们研究了它的两拷贝可重叠性问题，归结为某些投影Q与Schmidt秩二态的最大重叠不超过1/2。这种财产我们称之为半财产。我们首先表明，最大的重叠可以达到的向量，不是简单的产品形式，相对于两个副本之间的削减。然后，我们攻击的问题，在两个方面：a）证明了半性质的施密特秩二状态的一些类b）限制所需的重叠从上面的所有施密特秩二状态。我们已经成功地证明了半性质的广泛类的状态，并限制重叠从上述c<3/4。此外，我们将该问题转化为以下矩阵分析问题：将矩阵A \otimes I + I \otimes B的两个最大奇异值的平方和与A，B的无痕4 × 4矩阵绑定，并且Tr A^ \dagger A + Tr B^ \dagger B = 1/4。
