caa a22 4500 467905932 CHVBK 20180406152834.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10701-005-9006-z doi (NATIONALLICENCE)springer-10.1007/s10701-005-9006-z Compatibility of Subsystem States [Elektronische Daten] [Paul Butterley, Anthony Sudbery, Jason Szulc] We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of subsets of a set of qubits; in the case of three qubits we find quantum Bell inequalities—necessary conditions for a set of two-qubit states to be the reduced states of a mixed state of three qubits. We conjecture that these conditions are also sufficient. Springer Science+Business Media, Inc., 2006 Bell inequalities nationallicence multipartite quantum systems nationallicence Butterley Paul Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut Sudbery Anthony Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut Szulc Jason Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 83-101 0015-9018 36:1<83 2006 36 10701 https://doi.org/10.1007/s10701-005-9006-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-005-9006-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Butterley Paul Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut NATIONALLICENCE 700 1- Sudbery Anthony Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut NATIONALLICENCE 700 1- Szulc Jason Department of Mathematics, University of York, YO10 5DD, Heslington, York, England aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 83-101 0015-9018 36:1<83 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer