Speakers: Riccardo Laurenza, Mark Wilde

Опубликовано 3 февраля 2017, 19:30

1. Two-way assisted capacities for quantum and private communication 2. Converse bounds for private communication over quantum channels

"1. Quantum technologies promise reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks there is a crucial question to answer: What are their optimal rates without quantum repeaters? Our work solves this basic question for two remote parties connected by a quantum channel in the most relevant practical scenarios, without imposing any restriction on their classical communication, which can be unlimited and two-way. To achieve our results, we first extend the notion of relative entropy of entanglement from quantum states to channels, proving a general upper bound for all the two-way assisted capacities. Then, we design a technique, dubbed ""teleportation stretching"", which reduces the most general adaptive protocols for quantum or private communication to a simple block form. In this way, we can simplify our upper bound to a single-letter expression for many fundamental
channels, establishing exact formulas for the two-way assisted quantum capacities (Q2 = D2) and private capacities (P2 = K) of bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. These results have been achieved about 20 years after the first two-way capacity determined in [Bennett et al. PRL 78, 3217 (1997)]. In particular, we determine the fundamental rate-loss scaling which affects any quantum optical communication, e.g., for long-distance quantum key distribution, closing another long-standing open problem. By setting these limits, we establish the most general benchmarks for testing the performance of quantum repeaters. 2. This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a ""privacy test"" to establish a general meta-converse bound for private communication, which has a number of applications. The meta-converse allows for proving that any quantum channel's relative entropy of entanglement is a strong converse rate for private communication. For covariant channels, the meta-converse also leads to second-order expansions of relative entropy of entanglement bounds for private communication rates. For such channels, the bounds also apply to the private communication setting in which the sender and receiver are assisted by unlimited public classical communication, and as such, they are relevant for establishing various converse bounds for quantum key distribution protocols conducted over these channels. We find precise characterizations for several channels of interest and apply the methods to establish several converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels."