Remote information concentration and multipartite entanglement in multilevel systems

Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found, i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.Comment: 10 pages, 3 figure

Multipartite unlockable bound entanglement in the stabilizer formalism

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that if a set of commuting operators from the generalized Pauli group on $n$ qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state and its recent generalization to even number of qubits can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.Comment: 7 pages, no figur

Quantum network teleportation for quantum information distribution and concentration

We investigate the schemes of quantum network teleportation for quantum information distribution and concentration which are essential in quantum cloud computation and quantum internet. In those schemes, the cloud can send simultaneously identical unknown quantum states to clients located in different places by a network like teleportation with a prior shared multipartite entangled state resource. The cloud first perform the quantum operation, each client can recover their quantum state locally by using the classical information announced by the cloud about the measurement result. The number of clients can be beyond the number of identical quantum states intentionally being sent, this quantum network teleportation can make sure that the retrieved quantum state is optimal. Furthermore, we present a scheme to realize its reverse process, which concentrates the states from the clients to reconstruct the original state of the cloud. These schemes facilitate the quantum information distribution and concentration in quantum networks in the framework of quantum cloud computation. Potential applications in time synchronization are discussed.Comment: 7 pages, 1 figur

Quantum Cloning Machines and the Applications

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published online

Percolation Theories for Quantum Networks

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called ``concurrence percolation,'' which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design

Advances in High Dimensional Quantum Entanglement

Since its discovery in the last century, quantum entanglement has challenged some of our most cherished classical views, such as locality and reality. Today, the second quantum revolution is in full swing and promises to revolutionize areas such as computation, communication, metrology, and imaging. Here, we review conceptual and experimental advances in complex entangled systems involving many multilevel quantum particles. We provide an overview of the latest technological developments in the generation and manipulation of high-dimensionally entangled photonic systems encoded in various discrete degrees of freedom such as path, transverse spatial modes or time/frequency bins. This overview should help to transfer various physical principles for the generation and manipulation from one to another degree of freedom and thus inspire new technical developments. We also show how purely academic questions and curiosity led to new technological applications. Here fundamental research provides the necessary knowledge for coming technologies such as a prospective quantum internet or the quantum teleportation of all information stored in a quantum system. Finally, we discuss some important problems in the area of high-dimensional entanglement and give a brief outlook on possible future developments.Comment: Comments and suggestions for additional references are welcome! Updated affiliations onl

Entanglement and geometry in multipartite systems

Verschränkung ist eines der zentralsten Themen der Quantentheorie. Sie besitzt kein klassisches Äquivalent und war daher Thema kontroversieller Debatten seit fast einem Jahrhundert. Was über lange Zeit eine rein philosophische Debatte blieb, hat Heute ein neues Gebiet der Physik initiiert. Die Quanteninformationstheorie nimmt das Konzept der Verschränkung in der Natur ernst und hat seither neue Anwendungen, wie z.B. Quantenkryptographie oder den Quantencomputer, gefunden. Für diese praktischen Anwendungen ist Verschränkung die wichtigste Ressource, die es ermöglicht, dass die quanteninformationstheoretischen Anwendungen jedes klassische Gegenstück übertreffen. Allerdings ist diese Eigenschaft keineswegs gut verstanden. Selbst scheinbar einfache Probleme, wie die mathematische Unterscheidung zwischen verschränkten und separablen Zustanden, sind nach wie vor ungelöst. In dieser Arbeit behandeln wir intensiv die mathematische Theorie der Verschränkung. Wir waren in der Lage Techniken zu entwickeln, die die Detektion von Verschränkten Zuständen weiter verbessern, besonders in Vielteilchen-Systemen beliebiger Dimension. Außerdem waren wir in der Lage allgemeine Mengen von Verschränkungsmaßen zu entwickeln, die nicht nur Zweiteilchenverschränkung quantifizieren, sondern auch eine konsistente Quantifikation von Verschränkung in Vielteilchen-Systemen ermöglichen. Weiters haben wir berechenbare untere Schranken an diese Maße hergeleitet und gezeigt, dass diese nicht nur sehr effizient mittels vier dimensionaler Matrizen berechnet werden können, sondern auch in den meisten Fällen sehr knapp am wahren Wert liegen. Schlussendlich haben wir noch Techniken entwickelt und verbessert mit denen sich neu entwickelte Maße und Distillationsprozeduren gut testen lassen.Entanglement is at the heart of quantum theory. It has no classical counterpart and has therefore been subject of a controversial debate for almost a century. What has remained a purely philosophical debate for many decades has now sparked a whole new field in physics. Quantum information theory takes the concept of entanglement in nature seriously and has since offered novel applications such as e.g. quantum cryptography and quantum computing. For these practical applications entanglement is a crucial resource, which enables the quantum informational tasks to outperform any classical counterpart. However it is far from well understood. Even seemingly simple problems, such as the mathematical distinction between entangled states and separable ones, remain unsolved to date. In this work we intensively investigate the mathematical theory of entanglement. We were able to develop techniques to further improve the detection of entangled states, especially in multipartite systems of arbitrary dimension. Also we were able to provide general sets of entanglement measures, which not only quantify bipartite entanglement, but also give a consistent quantification of entanglement in multipartite systems. Furthermore we have derived computable lower bounds on these measures and have shown that they are not only computed very efficiently via four dimensional matrices but also very tight in most cases. Finally we have developed and improved techniques that serve as a testing ground for newly developed measures and distillation procedures