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A separability criterion is a necessary condition a state must satisfy to be separable. ... Quantum mechanics may be modelled on a projective Hilbert space, ...
In quantum mechanics, in particular quantum information, the Range criterion is a necessary condition that a state must satisfy in order to be separable. In other words, it is a separability criterion.
In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum-chemistry calculations changes with the system size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour when interaction between the involved molecular subsystems is nullified (for example, by distance).
A Werner state [1] is a × -dimensional bipartite quantum state density matrix that is invariant under all unitary operators of the form . That is, it is a bipartite quantum state ρ A B {\displaystyle \rho _{AB}} that satisfies
In quantum mechanics, negativity is a measure of quantum entanglement which is easy to compute. It is a measure deriving from the PPT criterion for separability. [1] It has been shown to be an entanglement monotone [2] [3] and hence a proper measure of entanglement.
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient.
In quantum information theory, the reduction criterion is a necessary condition a mixed state must satisfy in order for it to be separable. In other words, the reduction criterion is a separability criterion. It was first proved [1] and independently formulated in 1999. [2]
The algebra of observables in quantum mechanics is naturally an algebra of operators defined on a Hilbert space, according to Werner Heisenberg's matrix mechanics formulation of quantum theory. [25] Von Neumann began investigating operator algebras in the 1930s, as rings of operators on a Hilbert space.