Entanglement, CP-Maps and Quantum Communications

The 20th century has witnessed the rise of quantum mechanics and its fueled scientific and technological revolution. The humankind is now on the verge of a second quantum revolution sparked by quantum information science and engineering (QISE). Entanglement as a quintessential quantum resource lies at the heart of QISE, giving rise to a plethora of quantum-enabled or enhanced capabilities that shift the landscape of communication, sensing, and computing. This talk will focus on sensing and precision metrology enhanced by entanglement, a unique and radically new resource for information processing. I will describe our recent experimental advances in entanglement-based quantum machine learning for data classification and entangled sensor networks for precise radiofrequency and optomechanical sensing. A pathway toward large-scale quantum sensor networks and prospects for future applications underpinned by quantum-enhanced sensing will also be discussed.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers. In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques. The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.

Quantum entanglement is the most representative feature of quantum mechanics to classical mechanics. It is the delocalization, non-classical strong correlation among multiple quantum system. It has been developed for nearly one hundred years and a lot of methods of production and applications have been proposed. Aiming at the generation mode of quantum entanglement, this study presents two general preparation methods of quantum entanglement sources, including spontaneous parametric down-conversion (SPDC) and the preparation of quantum entanglement sources based on the four-wave mixing (FWM) effect. The principle, advantages and disadvantages of quantum entanglement sources are analyzed respectively. Finally, the research and application direction of the preparation method of quantum entanglement source are prospected. With the ability of preparation of quantum entanglement source, the application of quantum entanglement developed quickly, (e.g., quantum teleportation, entanglement swapping, quantum key distribution and quantum dense coding in the area of communication), and other area such as quantum computer, quantum imaging, quantum ranging and quantum clock synchronization. These results shed light on guiding further exploration of entanglement fabrication.

The architecture scalability afforded by recent proposals of a large scale photonic based quantum computer, utilizing the theoretical developments of topological cluster states and the photonic chip, allows us to move on to a discussion of massively scaled Quantum Information Processing (QIP). In this letter we introduce the model for a secure and unsecured topological cluster mainframe. We consider the quantum analogue of High Performance Computing, where a dedicated server farm is utilized by many users to run algorithms and share quantum data. The scaling structure of photonics based topological cluster computing leads to an attractive future for server based QIP, where dedicated mainframes can be constructed and/or expanded to serve an increasingly hungry user base with the ideal resource for individual quantum information processing.

Recent advances in pointing and tracking capabilities of small satellite platforms have enabled adoption of capabilities such as high-resolution Earth Observation (EO), inter-satellite laser communications and, more recently, quantum communications. Quantum communications requires unusually narrow optical beams and tight pointing performance (on the order of ten microradians) to close an inherently brightness-limited quantum link. This limit is due to quantum communication protocols such as quantum key distribution and teleportation requiring individual quantum states to be transmitted with photon number restrictions. We examine an opportunity to combine quantum communications with laser communications in sharing an optical link. We discuss a combined quantum and laser communication terminal capable of performing space-to-ground entanglement-distribution and high data rate communications on a 12U CubeSat with a 95mm beam expander and an 60 cm aperture optical ground telescope. Photon pairs produced by the quantum terminal are entangled in polarization so the polarization must be maintained throughout the optical link. We discuss active and passive compensation methods in space and polarization reference frame correction using a polarized reference beacon at the ground station. The combined quantum and laser communication terminal approach enables secure communications over an optical channel with rates of 100 Mbps and sub-nanosecond time transfer.

This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.

Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow for novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in Quantum Information Theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space, as well as the space of nonlocal correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that, for such systems, some of these questions become tractable. This PhD Thesis is dedicated to the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It contains original results in these four threads of research: PPT entanglement in the symmetric states, nonlocality detection in many-body systems, the non-equivalence between entanglement and nonlocality and elemental monogamies of correlations. First, we study PPT entanglement in fully symmetric n-qubit states. We solve the open question on the existence of four-qubit PPT entangled states of these kind, providing constructive examples and methods. Furthermore, we develop criteria for separability, edgeness and the Schmidt number of PPT entangled symmetric states. Geometrically, we focus on the characterization of extremal states of this family and we provide an algorithm to find states with such properties. Second, we study nonlocality in many-body systems. We consider permutationally and translationally invariant Bell inequalities consisting of two-body correlators. These constitute the first tools to detect nonlocality in many-body systems in an experimentally friendly way with our current technology. Furthermore, we show how these Bell inequalities detect nonlocality in physically relevant systems such as ground states of Hamiltonians that naturally arise e.g., in nuclear physics. We provide analytical classes of Bell inequalities and we analytically characterize which states and measurements are best suited for them. We show that the method we introduce can be fully generalized to correlators of any order in any Bell scenario. Finally, we provide some feedback from a more experimental point of view. Third, we demonstrate that entanglement and nonlocality are inequivalent concepts in general; a question that remained open in the multipartite case. We show that the strongest form of entanglement, genuinely multipartite entanglement, does not imply the strongest form of nonlocality, genuinely multipartite nonlocality, in any case. We give a constructive method that, starting from a multipartite genuinely multipartite state admitting a K-local model, extends it to a genuinely multipartite entangled state of any number of parties while preserving the degree of locality. Finally, we show that nonlocal correlations are monogamous in a much stronger sense than the typical one, in which the figure of merit compares a Bell inequality violation between two sets of parties. We show that the amount of Bell violation that a set of parties observes limits the knowledge that any external observer may gain on any of the outcomes of any of the parties performing the Bell experiment. We show that this holds even if such observer is not limited by quantum physics, but it only obeys the no-signalling principle. Apart from its fundamental interest, we show how these stronger monogamy relations boost the performance of some device-independent (DI) protocols such as DI quantum key distribution or DI randomness amplification.

Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable quantum resource remains an open issue. Here we study independently prepared identical particles showing that, when they spatially overlap, an operational entanglement exists that can be made manifest by means of separated localized measurements. We prove this entanglement is physical in that it can be directly exploited to activate quantum information protocols, such as teleportation. These results establish that particle indistinguishability is a utilizable quantum feature and open the way to new quantum-enhanced applications.

Pulse-based Electron–Nuclear and ELectron–electron DOuble Resonance (ENDOR/ELDOR) techniques have been applied to molecular spins in order to implement ensemble electron spin-qubit based quantum computers/computing (QC) and quantum information processing (QIP) in the solid state. Pulsed ENDOR-based QC/QIP experiments for super dense coding (SDC) have for the first time been carried out by the use of molecular electron- and nuclear-spin entities such as the stable malonyl radical as matter spin-qubits. The spin-qubit manipulation technology for quantum gate operations in this work is based on the time-proportional-phase-increment (TPPI) technique, enabling us to distinguish between the phases of spin-qubit based entangled states. The TPPI technique, as firstly applied by Mehring et al. (M. Mehring, J. Mende and W. Scherer, Phys. Rev. Lett., 2003, 90, 153001), has illustrated the establishment of quantum entanglement between electron- and nuclear-spin states and mutual interconversion between the electron–nuclear Bell states. The electron-spin 4π-periodicity in phase shows up in the QC/QIP experiments, explicitly and experimentally illustrating the electron-spin spinor nature for the first time. Tripartite QC experiments have been made, showing the occurrence of separable states. Also, the development of novel electron-spin technology to manipulate multi-electron spin-qubits is described. In this work, the pulsed coherent-dual ELDOR for QC/QIP has for the first time been implemented by invoking a novel microwave dual phase-rotation technique. Thus, applications of the coherent-dual ELDOR to molecular electron spin-qubit systems are also discussed, emphasising designing the molecular two electron-qubit systems appropriate for QC/QIP. g- and/or hyperfine A-tensor engineering approaches give us the two- and multi-electron-qubit systems, which have been a materials challenge to implement matter spin-qubit based QC/QIP. The targeted matter spin-qubits can be used to facilitate selective resonant microwave excitations achieved by the pulsed ELDOR technique. In addition to DiVincenzo's five criteria, general requisites for scalable electron spin-qubit systems as 1D periodic robust spin structures are described. According to the requisites, double- or triple-stranded helicates embedding open-shell metal cations are proposed instead of organic molecular spin-qubits.

Non-classical states of light, which include squeezed and entangled states of light, are the cornerstone of quantum mechanics and quantum information sciences. To date, non-classical states of light with much higher quality than before are required to develop high-fidelity quantum information processing and high-precision quantum metrology. Squeezed and entangled states with approximately 10 dB noise below the corresponding shot noise limit have been generated using a series of methods, which means that the noise variance reaches a few percent of the vacuum noise. Quantum teleportation, which means transferring an unknown quantum state from a sending station to a distant receiving station supported by entangled states, is the foundation of quantum computation and quantum communication networks. Quantum teleportation in continuous variable regions is unconditional because the entangled states used are always deterministic. The quantum teleportation distance was recently extended to the order of kilometers, which paves the way for constructing a practical quantum information network.

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

Teaching Quantum Computing with the QuIDE Simulator

Quantum information science is one of the frontier areas of science and technology. It is also an interdisciplinary area of research where scientists from physics, mathematics, and computer science can contribute alike. One of the main goals is how well one can process information using laws of quantum theory. Quantum information theory aims to process information that is not amenable with classical devices. At the same time this also provides new insights into the nature of the quantum world. Quantum information processing includes quantum computation, quantum communication, quantum cryptography and various information processing tasks. Not only does this provide a fundamental arena to investigate quantum phenomena but also gives new technological benefits like quantum teleportation, remote state preparation and secure communications. In India there is a growing interest in this emerging field. In view of this we had organized an International Program on Quantum Information (IPQI-2010) at the Institute of Physics, Bhubaneswar during January 4–January 30, 2010. In this programme, there were experts from all over the world and topics of focus were on various issues related to quantum information science and general quantum theory, characterization and quantification of entanglement, quantum channels and quantum operations, role of entanglement in quantum algorithms and quantum computation, developing new quantum algorithms, understanding of capacities of quantum channels, and new communication tasks in the multiparty case.

This chapter unifies all of the channel coding theorems that we have studied in this book. One of the most general information-processing tasks that a sender and receiver can accomplish is to transmit classical and quantum information and generate entanglement with many independent uses of a quantum channel and with the assistance of classical communication, quantum communication, and shared entanglement.1 The resulting rates for communication are net rates that give the generation rate of a resource less its consumption rate. Since we have three resources, all achievable rates are rate triples ( C,Q,E ) that lie in a three-dimensional capacity region, where C is the net rate of classical communication, Q is the net rate of quantum communication, and E is the net rate of entanglement consumption/generation. The capacity theorem for this general scenario is known as the quantum dynamic capacity theorem, and it is the main theorem that we prove in this chapter. All of the rates given in the channel coding theorems of previous chapters are special points in this three-dimensional capacity region. The proof of the quantum dynamic capacity theorem comes in two parts: the direct coding theorem and the converse theorem. The direct coding theorem demonstrates that the strategy for achieving any point in the three-dimensional capacity region is remarkably simple: we just combine the protocol from Corollary 22.5.2 for entanglement-assisted classical and quantum communication with the three unit protocols of teleportation, super-dense coding, and entanglement distribution. The interpretation of the achievable rate region is that it is the unit resource capacity region from Chapter 8 translated along the points achievable with the protocol from Corollary 22.5.2. In the proof of the converse theorem, we analyze the most general protocol that can consume and generate classical communication, quantum communication, and entanglement along with the consumption of many independent uses of a quantum channel, and we show that the net rates for such a protocol are bounded by the regularization of the achievable rate region.