Continuous-variable versus hybrid schemes for quantum teleportation of Gaussian states

In this paper, we examine and compare two fundamentally different teleportation schemes: the well-known continuous-variable scheme of Vaidman, Braunstein, and Kimble (VBK) and a recently proposed hybrid scheme by Andersen and Ralph (AR). We analyze the teleportation of ensembles of arbitrary pure single-mode Gaussian states using these schemes and see how they fare against the optimal measure-and-prepare strategies—the benchmarks. In the VBK case, we allow for nonunit gain tuning and additionally consider a class of non-Gaussian resources in order to optimize performance. The results suggest that the AR scheme may likely be a more suitable candidate for beating the benchmarks in the teleportation of squeezing, capable of achieving this for moderate resources in comparison to the VBK scheme. Moreover, our quantification of resources, whereby different protocols are compared at fixed values of the entanglement entropy or the mean energy of the resource states, brings into question any advantage due to non-Gaussianity for quantum teleportation of Gaussian states

Divide and Scale: Formalization of Distributed Ledger Sharding Protocols

Sharding distributed ledgers is the most promising on-chain solution for scaling blockchain technology. In this work, we define and analyze the properties a sharded distributed ledger should fulfill. More specifically, we show that a sharded blockchain cannot be scalable under a fully adaptive adversary, but it can scale up to $O(n/\log n)$ under an epoch-adaptive adversary. This is possible only if the distributed ledger creates succinct proofs of the valid state updates at the end of each epoch. Our model builds upon and extends the Bitcoin backbone protocol by defining consistency and scalability. Consistency encompasses the need for atomic execution of cross-shard transactions to preserve safety, whereas scalability encapsulates the speedup a sharded system can gain in comparison to a non-sharded system. We introduce a protocol abstraction and highlight the sufficient components for secure and efficient sharding in our model. In order to show the power of our framework, we analyze the most prominent shared blockchains (Elastico, Monoxide, OmniLedger, RapidChain) and pinpoint where they fail to meet the desired properties

Cuttlefish: Expressive Fast Path Blockchains with FastUnlock

Cuttlefish addresses several limitations of existing consensus-less and consensus-minimized decentralized ledgers, including restricted programmability and the risk of deadlocked assets. The key insight of Cuttlefish is that consensus in blockchains is necessary due to contention, rather than multiple owners of an asset as suggested by prior work. Previous proposals proactively use consensus to prevent contention from blocking assets, taking a pessimistic approach. In contrast, Cuttlefish introduces collective objects and multi-owner transactions that can offer most of the functionality of classic blockchains when objects transacted on are not under contention. Additionally, in case of contention, Cuttlefish proposes a novel `Unlock' protocol that significantly reduces the latency of unblocking contented objects. By leveraging these features, Cuttlefish implements consensus-less protocols for a broader range of transactions, including asset swaps and multi-signature transactions, which were previously believed to require consensus

Mandator and Sporades: Robust Wide-Area Consensus with Efficient Request Dissemination

Consensus algorithms are deployed in the wide area to achieve high availability for geographically replicated applications. Wide-area consensus is challenging due to two main reasons: (1) low throughput due to the high latency overhead of client request dissemination and (2) network asynchrony that causes consensus protocols to lose liveness. In this paper, we propose Mandator and Sporades, a modular state machine replication algorithm that enables high performance and resiliency in the wide-area setting. To address the high client request dissemination overhead challenge, we propose Mandator, a novel consensus-agnostic asynchronous dissemination layer. Mandator separates client request dissemination from the critical path of consensus to obtain high performance. Composing Mandator with Multi-Paxos (Mandator-Paxos) delivers significantly high throughput under synchronous networks. However, under asynchronous network conditions, Mandator-Paxos loses liveness which results in high latency. To achieve low latency and robustness under asynchrony, we propose Sporades, a novel omission fault-tolerant consensus algorithm. Sporades consists of two modes of operations -- synchronous and asynchronous -- that always ensure liveness. The combination of Mandator and Sporades (Mandator-Sporades) provides a robust and high-performing state machine replication system. We implement and evaluate Mandator-Sporades in a wide-area deployment running on Amazon EC2. Our evaluation shows that in the synchronous execution, Mandator-Sporades achieves 300k tx/sec throughput in less than 900ms latency, outperforming Multi-Paxos, EPaxos and Rabia by 650\% in throughput, at a modest expense of latency. Furthermore, we show that Mandator-Sporades outperforms Mandator-Paxos, Multi-Paxos, and EPaxos in the face of targeted distributed denial-of-service attacks

Entanglement, Einstein-Podolsky-Rosen steering and cryptographical applications

This PhD Dissertation collects results of my own work on the topic of continuous variable (CV) quantum teleportation, which is one of the most important applications of quantum entanglement, as well as on the understanding, quantification, detection, and applications of a type of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering, for both bipartite and multipartite systems and with a main focus on CV systems. For the first results, we examine and compare two fundamentally different teleportation schemes; the well-known continuous variable scheme of Vaidman, Braunstein and Kimble, and a recently proposed hybrid scheme by Andersen and Ralph. We analyse the teleportation of ensembles of arbitrary pure single-mode Gaussian states using these schemes and compare their performance against classical strategies that utilize no entanglement (benchmarks). Our analysis brings into question any advantage due to non-Gaussianity for quantum teleportation of Gaussian states. For the second part of the results, we study bipartite EPR-steering. We propose a novel powerful method to detect steering in quantum systems of any dimension in a systematic and hierarchical way. Our method includes previous results of the literature as special cases on one hand, and goes beyond them on the other. We proceed to the quantification of steering-type correlations, and introduce a measure of steering for arbitrary bipartite Gaussian states, prove many useful properties, and provide with an operational interpretation of the proposed measure in terms of the key rate in one-sided device independent quantum key distribution. Finally, we show how the Gaussian steering measure gives a lower bound to a more general quantifier of which Gaussian states are proven to be extremal. We proceed to the study of multipartite steering, and derive laws for the distribution of Gaussian steering among different parties in multipartite Gaussian states. We define an indicator of collective steering-type correlations, which is interpreted operationally in terms of the guaranteed secret key rate in the multi-party cryptographic task of quantum secret sharing. The final results look at the cryptographical task of quantum secret sharing, whose security has remained unproven almost two decades after its original conception. By utilizing intuition and ideas from steering, we manage to establish for the first time an unconditional security proof for CV entanglement-based quantum secret sharing schemes, and demonstrate their practical feasibility. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies