Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].Comment: An extended abstract version of this result appears in the proceedings of 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

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.Comment: accepted for publication in Physical Review

Achieving minimum-error discrimination of an arbitrary set of laser-light pulses

Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a fundamental limit on how well different coher- ent states can be distinguished, even with perfect detectors, and limits such discrimination to have a finite minimum probability of error. While conventional optical receivers lead to error rates well above this fundamental limit, Dolinar found an explicit receiver design involving optical feedback and photon counting that can achieve the minimum probability of error for discriminating any two given coherent states. The generalization of this construction to larger sets of coherent states has proven to be challenging, evidencing that there may be a limitation inherent to a linear-optics-based adaptive measurement strategy. In this Letter, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multi-copy quantum hypotheses (arXiv:1201.6625) and properties of coherent states. Furthermore, our construction is reusable, composable, and applicable to designing quantum-limited processing of coherent-state signals to optimize any metric of choice. As illustrative examples, we analyze the performance of discriminating a ternary alphabet, and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.Comment: 9 pages, 2 figures; v2 Minor correction