本文提出利用量子克隆生成三方量子网络，并通过扩展 Finner 不等式、三方互信息及挤压纠缠区分克隆网络与独立纠缠源网络。
摘要：
随着量子技术的进步，量子网络领域已成为一个重要的研究方向。在过去几年中，人们在理解量子网络中存在的关联方面取得了实质性进展。在本文中，我们研究克隆作为生成三方量子网络的一种有前景的方法，这些网络还可进一步用于创建更大的网络。我们分析了可利用克隆变换创建的各种量子网络拓扑。这在纠缠对可用性受限的情况下将十分有用。除此之外，我们聚焦于区分由克隆创建的网络与通过分发独立生成的纠缠对所创建的网络这一问题。我们发现，有若干状态无法以标准方式利用 Finner 不等式加以区分。针对此类状态，我们根据网络拓扑，通过将观察者数量从三个进一步增加到四个或六个，对现有的三角形网络 Finner 不等式提出了一种扩展。该扩展考虑了克隆网络情形中存在的额外关联。在文章最后一部分，我们使用三方互信息来区分克隆网络与由独立源创建的网络，并进一步使用挤压纠缠作为度量，来量化克隆网络中的依赖程度。
英文摘要：
With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.
We consider probabilistic cloning of a state chosen from a mutually nonorthogonal set of pure states, with the help of a party holding supplementary information in the form of pure states. When the number of states is 2, we show that the best efficiency of producing m copies is always achieved by a two-step protocol in which the helping party first attempts to produce m-1 copies from the supplementary state, and if it fails, then the original state is used to produce m copies. On the other hand, when the number of states exceeds two, the best efficiency is not always achieved by such a protoco…
Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying superposition of multiple clones simultaneously. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI). For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. F…
The efficacies of maximally and that of non-maximally entangled mixed states as teleportation channels have been studied. A new class of non-maximally entangled mixed states have been proposed also. Their advantages as quantum teleportation channels over existing non-maximally entangled mixed states have been verified. The mixed states can also be generated using quantum cloning machines. We have also studied how one can utilize the mixed entangled states obtained as output from a state independent quantum cloning machine in teleportation and dense coding. Mixed states can also be used in secr…
We propose a physically realizable machine which can either generate multiparticle W-like states, or implement high fidelity $1 \to M$ ($M=1,2,... \infty$) anti-cloning of an arbitrary qubit state, in a single step. Moreover this universal machine acts as a catalyst in that it is unchanged after either procedure, effectively resetting itself for its next operation. It also possesses an inherent {\em immunity} to decoherence. Most importantly in terms of practical multi-party quantum communication, the machine's robustness in the presence of decoherence actually {\em increases} as the number of…
Generalizing Amari's work titled "Information geometry on hierarchy of probability distributions", we define the degrees of irreducible multiparty correlations in a multiparty quantum state based on quantum relative entropy. We prove that these definitions are equivalent to those derived from the maximal von Neaumann entropy principle. Based on these definitions, we find a counterintuitive result on irreducible multiparty correlations: although the degree of the total correlation in a three-party quantum state does not increase under local operations, the irreducible three-party correlation ca…
Einstein-Podolsky-Rosen (EPR) steering allows two parties to verify their entanglement, even if one party's measurements are untrusted. This concept has not only provided new insights into the nature of non-local spatial correlations in quantum mechanics, but also serves as a resource for one-sided device-independent quantum information tasks. Here, we investigate how EPR steering behaves when one-half of a maximally-entangled pair of qudits (multidimensional quantum systems) is cloned by a universal cloning machine. We find that EPR steering, as verified by a criterion based on the mutual inf…
Einstein-Podolsky-Rosen (EPR) steering is the explicit demonstration of the fact that the measurements of one party can in influence the quantum state held by another, distant, party, and do so even if the measurements themselves are untrusted. This has been shown to allow one-sided device-independent quantum-information tasks between two remote parties. However, in general, advanced multiparty protocols for generic quantum technologies, such as quantum secret sharing and blind quantum computing for quantum networks, demand multipartite quantum correlations of graph states shared between more …
Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that unconditionally secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. In this paper, the scope of this general impossibility proof is analyzed, and gaps are found. Two variants of a bit commitment scheme utilizing anonymous quantum states and d…
Encrypted Cloning, Absolute Maximal Entanglement and Quantum Secret Sharing
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）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Quantum Bridge Technologies Inc.（量子桥技术有限公司）；University of Toronto（多伦多大学）；Department of Electrical and Computer Engineering, University of Toronto（多伦多大学电气与计算机工程系）
Secure two-party computation considers the problem of two parties computing a joint function of their private inputs without revealing anything beyond the output. In this work, we consider the setting where the two parties (a classical Alice and a quantum Bob) can communicate only via a classical channel. Our first result shows that it is in general impossible to realize a two-party quantum functionality with black-box simulation in the case of malicious quantum adversaries. In particular, we show that the existence of a secure quantum computing protocol that relies only on classical channels …
The problem of quantum state reduction in the process of measurement has attracted attention of almost everyone who created, developed or explained quantum physics to the students. Absence of a solution is the basis for the statement that the physical laws alone are not enough to describe the reduction of state of the measured particle. In the presented study, it is taken into account that the measurement of all properties of quantum particles can not be carried out in one physical process (the no-cloning theorem). For such a measurement several series of incompatible observations are needed, …
Full characterization of informative subsets in Quantum Encrypted Cloning
Università degli Studi di Milano-Bicocca（米兰比可卡大学）；Università degli Studi di Milano（米兰大学）；Università Cattolica del Sacro Cuore（天主教神圣之心大学）；Institut National des Sciences Appliquées de Lyon（里昂国立应用科学学院）
We develop a framework which unifies seemingly different extension (or "joinability") problems for bipartite quantum states and channels. This includes well known extension problems such as optimal quantum cloning and quantum marginal problems as special instances. Central to our generalization is a variant of the Choi-Jamiolkowski isomorphism between bipartite states and dynamical maps which we term the "homocorrelation map": while the former emphasizes the preservation of the positivity constraint, the latter is designed to preserve statistical correlations, allowing direct contact with enta…
Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator
We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum…
Limits on Broadcasting Genuine Multipartite Entanglement in Quantum Networks
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
In this work we propose the generation of a hybrid entangled resource (HER) and its further application in a quantum teleportation scheme from an experimentally feasible point of view. The source for HER preparation is based on the four wave mixing process in a photonic crystal fiber, from which one party of its output bipartite state is used to herald a single photon or a single photon added coherent state. From the heralded state and linear optics the HER is created. In the proposed teleportation protocol Bob uses the HER to teleport qubits with different spectral properties. Bob makes a Bel…
Entangled quantum particles have correlations stronger than those allowed by classical physics. These correlations are the focus of of the deepest issues in quantum mechanics [1-3] and are the basis of many quantum technologies. The entanglement of discrete particle properties has been studied extensively in the context of quantum computing [4], cryptography [5], and quantum repeaters [6] while entanglement between the continuous properties of particles may play a critical role in improving the sensitivity of gravitational wave detectors [7,8], atomic clocks [9], and other high precision instr…
This paper presents a physical mapping tool for quantum circuits, which generates the optimal Universal Logic Block (ULB) that can perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influ…
