Final Report Summary - QOLAPS (Quantum resources: conceptuals and applications) The project QOLAPS focused on fundamental research concerning the theory and implementation of quantum resources: quantum entanglement, non-locality and quantum contextuality. We have made a series of breaktroughs in deciphering of the rich structure of quantum resources and their possible applications. Below we state major results concerning the above three topics and related ones.Entanglement• A fundamental no-go result was proved – there exist bound entangled states whose secret key cannot be used efficiently on large distances by any quantum key repeater.• Contrary to the false counterexamples, we showed that arbitrary states in 1D chain which has exponential decaying correlations, satisfy the area law.• Tasks for which transmission of a quantum system is a more powerful resource than entanglement-assisted classical communication were showed. • A highly efficient method for quantum state estimation and multipartite entanglement detections was developed. Our methods are helpful for, e.g. metrology task, or establishing the status of non-local networks.• A multipartite entanglement detection with minimal effort was achieved.• For the first time the geometric invariant theory was successfully applied to classification of entanglement.Non-locality and Contextuality• We found the first protocols that amplify arbitrarily weak randomness by use of a fixed number of devices at a constant noise rate. This opened a possibility to amplify arbitrary weak randomness in labs. • We also achieved major steps towards a device-independent scheme with application in quantum cryptography. In particular, we report on experimental demonstration of the measurement-device-independent entanglement detection using witness method for general two qubits photon polarization systems. • The general connection between quantum advantage in communication complexity and Bell nonlocality was shown.• Novel methods to construct genuinely n-partite entangled states, without any n-partite correlations, that do violate Bell inequalities were introduced. • We showed and experimentally demonstrated that the power of reduction of communication complexity can be harnessed to gain an advantage in a famous, immensely popular, card game - bridge. • High-level quantum random access codes were showed to enable larger advantages over the corresponding random access codes.• We introduced a scheme to quantify contextuality, as well as studying it as a resource.• It was proved that no nontrivial extremal point of the polytope of non-signaling correlations admits quantum realization.• We proved that the sensitivity of the ground state of Hamiltonian to unknown parameter can exhibit super – Heisenberg behavior which can be measured by magnetization parameter.The outcome of QOLAPS goes beyond its main topic, including among others, important issues of the emergence of objectivity, uncertainty relations, the resource of quantum steering and non-existence of a universal superposing machine. Some of them we list below.• We provided the first rigorous definition of objectivity in terms of states and identified the so-called state broadcasting structure. • We showed that some signature of objectivity is generic. • An uncertainty constrained principle was proposed as a physical principle which applies to single system and rules out a series of unphysical theories.• We constructed steering inequalities which, in contrast to Bell inequalities, exhibit unbounded violation and we provided experimentally feasible signature of unbounded violation of a steering inequality.• A no-go theorem was proved: one cannot create a superposition of unknown states unless there is some a priori knowledge. This result was subsequently implemented experimentally by another groups. • A novel multiparty secret sharing protocol was introduced which has huge advantages in scalability and can be realized with state-of-the-art technology.