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Register a new userUnconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
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We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We show a simple example of the broadcast QKD protocol overcoming the limit of the point-to-point strategy. Our result is thus an important step toward opening a new framework of network channel-based quantum communication technology.
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Bosonic channels are important in practice as they form a simple model for free-space or fiber-optic communication. Here we consider a single-sender two-receiver pure-loss bosonic broadcast channel and determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. We show how the state merging protocol leads to achievable rates in this setting, giving an inner bound on the capacity region. We also evaluate an outer bound on the region by using the relative entropy of entanglement and a `reduction by teleportation technique. The outer bounds match the inner bounds in the infinite-energy limit, thereby establishing the unconstrained capacity region for such channels. Our result could provide a useful benchmark for implementing a broadcasting of entanglement and secret key through such channels. An important open question relevant to practice is to determine the capacity region in both this setting and the single-sender single-receiver case when there is an energy constraint on the transmitter.
Quantum key distribution (QKD) is one of the most important subjects in quantum information theory. There are two kinds of QKD protocols, prepare-measure protocols and entanglement-based protocols. For long-distance communications in noisy environments, entanglement-based protocols might be more reliable since they could be assisted with distillation procedures to prevent from noises. In this paper, we study the entanglement-based QKD over certain noisy channels and present schemes against collective noises, including collective dephasing and collective rotation, Pauli noises, amplitude damping noises, phase damping noises and mixtures of them. We focus on how to implement QKD protocols over noisy channels as in noiseless ones without errors. We also analyze the efficiency of the schemes, demonstrating that they could be more efficient than the standard entanglement-based QKD scheme.
Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.
We derive a sufficient condition for advantage distillation to be secure against collective attacks in device-independent quantum key distribution (DIQKD), focusing on the repetition-code protocol. In addition, we describe a semidefinite programming method to check whether this condition holds for any probability distribution obtained in a DIQKD protocol. Applying our method to various probability distributions, we find that advantage distillation is possible up to depolarising-noise values of $q approx 9.1%$ or limited detector efficiencies of $eta approx 89.1%$ in a 2-input 2-output scenario. This exceeds the noise thresholds of $q approx 7.1%$ and $eta approx 90.7%$ respectively for DIQKD with one-way error correction using the CHSH inequality, thereby showing that it is possible to distill secret key beyond those thresholds.
The security of quantum key distribution has traditionally been analyzed in either the asymptotic or non-asymptotic regimes. In this paper, we provide a bridge between these two regimes, by determining second-order coding rates for key distillation in quantum key distribution under collective attacks. Our main result is a formula that characterizes the backoff from the known asymptotic formula for key distillation -- our formula incorporates the reliability and security of the protocol, as well as the mutual information variances to the legitimate receiver and the eavesdropper. In order to determine secure key rates against collective attacks, one should perform a joint optimization of the Holevo information and the Holevo information variance to the eavesdropper. We show how to do so by analyzing several examples, including the six-state, BB84, and continuous-variable quantum key distribution protocols (the last involving Gaussian modulation of coherent states along with heterodyne detection). The technical contributions of this paper include one-shot and second-order analyses of private communication over a compound quantum wiretap channel with fixed marginal and key distillation over a compound quantum wiretap source with fixed marginal. We also establish the second-order asymptotics of the smooth max-relative entropy of quantum states acting on a separable Hilbert space, and we derive a formula for the Holevo information variance of a Gaussian ensemble of Gaussian states.
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