Abstract
By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.
Highlights
Quantum entropy or Von Neumann entropy, which is a counterpart of the classical Shannon entropy, is an important subject in quantum information theory ([1])
The classical logics can be described by the Boolean algebras and the quantum logics can be described by the orthomodular lattices ([2,3,4,5])
The classical probability or Shannon entropy was based on the classical logics and quantum en
Summary
Quantum entropy or Von Neumann entropy, which is a counterpart of the classical Shannon entropy, is an important subject in quantum information theory ([1]). Example 2.2([4,5]) Let H be a complex Hilbert space, P (H) be the set of all orthogonal projection operators on H, P1, P2 ∈ P (H). In [2], the author defined the following three concepts: Let (L, ≤) be an orthomodular lattice and s be a state of (L, ≤), {a1, a2, · · · , an} be a finite orthogonal subset of L.
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