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We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of several fundamental channels, including the bosonic lossy channel. We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein-Kimble teleportation protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution.

In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information. DOI: 10.1103/PhysRevLett.113.140405 PACS numbers: 03.65.Ta, 03.67.Mn, 42.50.-p Quantum correlations represent a fundamental resource in quantum information and computation [1,2]. If we restrict the description of a quantum system to pure states, then quantum entanglement is synonymous with quantum correlations. However, this is not exactly the case when general mixed states are considered: Separable mixed states can still have residual correlations which cannot be simulated by any classical probability distribution [3,4]. These residual quantum correlations are today quantified by quantum discord [5].Quantum discord is defined as the difference between the total correlations within a quantum state, as measured by the quantum mutual information, and its classical correlations, corresponding to the maximal randomness which can be shared by two parties by means of local measurements and one-way classical communication [6]. This definition not only provides a more precise characterization of quantum correlations but also has direct application in various protocols, including quantum state merging [7], remote state preparation [8], discrimination of unitaries [9], quantum channel discrimination [10], quantum metrology [11], and quantum cryptography [12].For bosonic systems, like the optical modes of the electromagnetic field, it is therefore crucial to compute the quantum discord of Gaussian states [13]. Despite these states being the most common in experimental quantum optics and the most studied in continuous-variable quantum information [14], no closed formula is yet known for their quantum discord. What is computed is an upper bound, known as Gaussian discord [15,16], which is a simplified version based on Gaussian detections only. Gaussian discord has been conjectured to be the actual discord for Gaussian states, as also supported by recent numerical studies [17,18].In this Letter, we connect this conjecture on Gaussian discord with the recently solved conjecture on the bosonic minimum output entropy [19], according to which the von Neumann entropy at the output of a single-mode Gaussian channel is minimized by a pure Gaussian state at the input [13]. In particular, this optimal input state is the vacuum, or any other coherent state, when we consider Gaussian c...

We consider the continuous-variable protocol of Pirandola et al. [Nature Photonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strategies against the quantum links explicitly showing that, at fixed transmissivity and thermal noise, two-mode coherent attacks are optimal, manifestly outperforming one-mode collective attacks based on independent entangling cloners. Such an advantage is shown both in terms of security threshold and secret-key rate.