ON THE ORTHOCOMPLEMENTATION OF STATE-PROPERTY-SYSTEMS OF CONTEXTUAL SYSTEMS

We prove that strong subadditibity(SSA) of entropy holds for fermion systems. Main resultProbably,strong subadditibity(SSA) is the one of the most powerful prop- erties of entropy.In this paper, we prove SSA holds for fermion systems.We consider Fermonic systems on an integer lattice $\mathrm{Z}^{d},\mathrm{t}\mathrm{h}\mathrm{e}$ set of $\mathrm{d}$ -tuples of integers.The creation and annihilation operators will be denoted by $a_{j}^{*}$ and $a_{j}(j\in \mathrm{Z}^{d})$ .They satisfy the canonical anticommutation relations,We prove that strong subadditibity(SSA) of entropy holds for fermion systems. Main resultProbably,strong subadditibity(SSA) is the one of the most powerful prop- erties of entropy.In this paper, we prove SSA holds for fermion systems.We consider Fermonic systems on an integer lattice $\mathrm{Z}^{d},\mathrm{t}\mathrm{h}\mathrm{e}$ set of $\mathrm{d}$ -tuples of integers.The creation and annihilation operators will be denoted by $a_{j}^{*}$ and $a_{j}(j\in \mathrm{Z}^{d})$ .They satisfy the canonical anticommutation relations,

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Closure structures and orthocomplementation of state-property-systems of contextual systems.

Bart D’Hooghe

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Diederik Aerts, Didier Deses

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\mathrm{Z}^{d},\mathrm{t}\mathrm{h}\mathrm{e}

set of

\mathrm{d}

-tuples of integers.The creation and annihilation operators will be denoted by

a_{j}^{*}

and

a_{j}(j\in \mathrm{Z}^{d})

.They satisfy the canonical anticommutation relations,