title: No Quantum Realization of Extremal No-Signaling Boxes.
abstract: The study of quantum correlations is important for fundamental reasons as well as for quantum communication and information processing tasks. On the one hand, it is of tremendous interest to derive the correlations produced by measurements on separated composite quantum systems from within the set of all correlations obeying the no-signaling principle of relativity, by means of information-theoretic principles. On the other hand, an important ongoing research program concerns the formulation of device-independent cryptographic protocols based on quantum nonlocal correlations for the generation of secure keys, and the amplification and expansion of random bits against general no-signaling adversaries. In both these research programs, a fundamental question arises: Can any measurements on quantum states realize the correlations present in pure extremal no-signaling boxes? Here, we answer this question in full generality showing that no nontrivial (not local realistic) extremal boxes of general no-signaling theories can be realized in quantum theory. We then explore some important consequences of this fact.
authors: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland.|Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.
authors: Ravishankar
authors: R
authors: Ramanathan
authors: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland.|Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdansk, Poland.
authors: Jan
authors: J
authors: Tuziemski
authors: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland.|Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.
authors: Michał
authors: M
authors: Horodecki
authors: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland.|Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdansk, Poland.
authors: Paweł
authors: P
authors: Horodecki