Marek Winczewski

Entanglement is an intriguing quantum phenomenon with crucial implications for both fundamental physics and technological applications, e.g., quantum key distribution (QKD). In this paper, we show that multipartite private states from which secret keys are directly accessible to trusted partners are genuinely multipartite entangled states. With application to secure Quantum Internet, we consider the most general setup of multipartite quantum process (channel) in a network setting: multiplex quantum channel with involved parties having one of the three possible roles-- that of only sender or receiver, or both sender and receiver. We derive divergence-based measures for entangling abilities of multipartite quantum channels. We describe an LOCC-assisted secret key agreement (SKA) protocol for generation or distillation of key (private random bits) among multiple trusted allies connected through a quantum multiplex channel secure against a quantum eavesdropper, of which measurement-device-independent QKD and SKA protocols over quantum network laced with key repeaters are particular instances. We are able to provide upper bounds on the non-asymptotic private capacities, maximum rate at which secret key can be distilled via finite uses of channels, and lower bounds on asymptotic capacities. These bounds are expressed in terms of the divergence-based entanglement measures of the channels. Some of these measures lead to strong converse bounds on the private capacities. Our upper bounds on the private capacities also are upper bound on the multipartite quantum capacities where goal is to distill Greenberger{Horne{Zeilinger (GHZ) state. Also, we are able to derive upper bound on the secret key bits that can be distilled via LOCC among trusted allies sharing finite copies of multipartite quantum states.

We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We formulate a security condition for the considered class of protocols, that is based on the newly introduced non-signaling norm. This norm takes supremum over certain operations, that can be used to discriminate devices. It is shown that the security condition based on this norm, is equivalent to two security conditions present in the literature. We employ the idea of ``squashing" on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that squashed secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called ``squashed non-locality", has been constructed. It exhibits several important properties, including convexity, monotonicity, and additivity on tensor products. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the squashed non-locality is zero. Therefore one can not distill key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR less than 80%. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension. This extension provides the ultimate eavesdropping power with the minimal consumption of eavesdropper's memory and, as we prove, yields equivalent security conditions as previously known in the literature.