Classical theories with entanglement
| Autor: | D'Ariano, Giacomo Mauro, Erba, Marco, Perinotti, Paolo |
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| Rok vydání: | 2019 |
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| Zdroj: | Phys. Rev. A 101, 042118 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.101.042118 |
| Popis: | We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories---including the classical ones---can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that---under the hypothesis of $n$-local discriminability---no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex. Comment: The definitions of simplicial and classical theories have been relaxed, in order to include the non-convex cases; the results hold also in the non-convex cases. Improved and extended presentation. Added results on superposition and purification. Enhanced the 'Discussion and Conclusions' section. Minor corrections. Layout fixed and mention to Ref. [13] corrected |
| Databáze: | arXiv |
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