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Compatibility of Subsystem States

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of York, Heslington, York, YO10 5DD, England

    Paul Butterley, Anthony Sudbery & Jason Szulc

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  1. Paul Butterley
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  2. Anthony Sudbery
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  3. Jason Szulc
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Correspondence to Paul Butterley.

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Butterley, P., Sudbery, A. & Szulc, J. Compatibility of Subsystem States. Found Phys 36, 83–101 (2006). https://doi.org/10.1007/s10701-005-9006-z

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  • DOI: https://doi.org/10.1007/s10701-005-9006-z

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