On the Capacity Region of Bipartite and Tripartite Entanglement Switching and Key Distribution

International audienc

Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence

We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communication and defines a measure of genuine tripartite entanglement. We analytically determine the residual contangle for arbitrary pure three-mode Gaussian states and study the distribution of quantum correlations for such states. This will lead us to show that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/$W$ states of continuous variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the $W$ states of three qubits. We finally consider the action of decoherence on tripartite entangled Gaussian states, studying the decay of the residual contangle. The GHZ/$W$ states are shown to be maximally robust under both losses and thermal noise.Comment: 20 pages, 5 figures. (v2) References updated, published versio

Performance Evaluation of Classical and Quantum Communication Systems

The Transmission Control Protocol (TCP) is a robust and reliable method used to transport data across a network. Many variants of TCP exist, e.g., Scalable TCP, CUBIC, and H-TCP. While some of them have been studied from empirical and theoretical perspectives, others have been less amenable to a thorough mathematical analysis. Moreover, some of the more popular variants had not been analyzed in the context of the high-speed environments for which they were designed. To address this issue, we develop a generalized modeling technique for TCP congestion control under the assumption of high bandwidth-delay product. In a separate contribution, we develop a versatile fluid model for congestion-window-based and rate-based congestion controllers that can be used to analyze a protocol’s stability. We apply this model to CUBIC – the default implementation of TCP in Linux systems – and discover that under a certain loss probability model, CUBIC is locally asymptotically stable. The contribution of this work is twofold: (i) the first formal stability analysis of CUBIC, and (ii) the fluid model can be easily adapted to other protocols whose window or rate functions are difficult to model. We demonstrate another application of this model by analyzing the stability of H-TCP, another popular variant used in data science networks. On a different front, a wide range of quantum distributed applications, which either promise to improve on existing classical applications or offer functionality that is entirely unobtainable via classical means, are helping to fuel rapid technological advances in the area of quantum communication. In view of this, it is prudent to model and analyze quantum networks, whose applications range from quantum cryptography to quantum sensing. Several types of quantum distributed applications, such as the E91 protocol for quantum key distribution, make use of entanglement to meet their objectives. Thus, being able to distribute entanglement efficiently is one of the most important and fundamental tasks that must be performed in a quantum network – without this functionality, many quantum distributed applications would be rendered infeasible. Modeling such systems is vital in order to better conceptualize their operation, and more importantly, to discover and address the challenges involved in actualizing them. To this end, we explore the limits of star-topology entanglement switching networks and introduce methods to model the process of entanglement generation, a set of switching policies, memory constraints, link heterogeneity, and quantum state decoherence for a switch that can serve bipartite (and in a specific case, tripartite) entangled states. In one part of this work, we compare two modeling techniques: discrete time Markov chains (DTMCs) and continuous-time Markov chains (CTMCs). We find that while DTMCs are a more accurate way to model the operation of an entanglement distribution switch, they quickly become intractable when one introduces link heterogeneity or state decoherence into the model. In terms of accuracy, we show that not much is lost for the case of homogeneous links, infinite buffer and no decoherence when CTMCs are employed. We then use CTMCs to model more complex systems. In another part of this work, we analyze a switch that can store one or two qubits per link and can serve both bipartite and tripartite entangled states. Through analysis, we discover that randomized policies allow the switch to achieve a better capacity than time-division multiplexing between bipartite and tripartite entangling measurements, but the advantage decreases as the number of links grows

A throughput optimal scheduling policy for a quantum switch

We study a quantum switch that creates shared end-to-end entangled quantum states to multiple sets of users that are connected to it. Each user is connected to the switch via an optical link across which bipartite Bell-state entangled states are generated in each time-slot with certain probabilities, and the switch merges entanglements of links to create end-to-end entanglements for users. One qubit of an entanglement of a link is stored at the switch and the other qubit of the entanglement is stored at the user corresponding to the link. Assuming that qubits of entanglements of links decipher after one time-slot, we characterize the capacity region, which is defined as the set of arrival rates of requests for end-to-end entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a Max-Weight scheduling policy and show that it stabilizes the switch for all arrival rates that lie in the capacity region. We also provide numerical results to support our analysis

Bell nonlocality

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools which have been developed to describe and study the nonlocality of quantum theory, and which have raised this topic to the status of a full sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio

Correlation harvesting in the presence of Unruh and Hawking effects

Quantum field theory (QFT) in curved spacetime is a study of quantum fields under the influence of the relativistic motion of particles or spacetime curvature. The famous outcomes of this subject are the Unruh and Hawking effects. The Unruh effect claims that a uniformly accelerating atom (people in the community tend to use a model called the Unruh-DeWitt (UDW) particle detector, which is a two-level quantum system coupled to a quantum field) thermalizes even though an inertial observer sees no particles. That is, an acceleration motion excites the internal degree of freedom of the atom in such a way that the atom experiences as if it is immersed in a thermal bath. The Hawking effect is a phenomenon where a black hole radiates thermal quanta. If one puts a UDW detector outside an event horizon, then it also perceives thermality. Both the Unruh and Hawking effects show thermality, which is the core theme of this thesis. In recent years, a protocol called entanglement harvesting has attracted great interest. Entanglement harvesting utilizes multiple UDW detectors to extract (or ‘harvest’) entanglement pre-existed in a quantum field. The extracted entanglement is influenced by the geometry of spacetime and the trajectories of UDW detectors. One can also extract other types of correlations, and so we collectively call this the correlation harvesting protocol. In this thesis, we examine how thermal effects influence the ability of correlation harvesting. In a previous study, the case of two inertial UDW detectors coupled to a thermal quantum field was investigated. It was shown that as the temperature of the field increases, the extracted entanglement between the detectors decreases while the quantum mutual information (the total correlations including classical and quantum correlations) increases. Since a single detector in uniform acceleration motion or hovering near a black hole experiences thermality as if it is immersed in a thermal quantum field, it is natural to ask if harvested correlations also behave in the same manner. In contrast, we show that (i) the Unruh temperature of uniformly accelerating detectors prevents the detectors from extracting any correlations at the high temperatures, i.e., even the quantum mutual information vanishes at the extreme Unruh temperatures; (ii) high black hole temperatures also prevent the detectors from harvesting correlations, and this is no exception even for tripartite entanglement; and (iii) freely falling detectors in a black hole spacetime are less affected by this, and they have no trouble extracting correlations from the field even when detectors are causally disconnected by an event horizon