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Λ(ρ)\Lambda(\rho)

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Λ†\Lambda^\dagger is positive because Λ\Lambda is completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state; it is unital, Λ†(Ic)\Lambda^\dagger(I_c) = IfI_f , because Λ\Lambda preserves trace for every input. This duality is the same construction Stinespring used to show that any completely positive map admits a dilation to a larger, unitary description [ 9 ] , and it lets a coarse Hamiltonian be pulled back onto the fine space without the fine space’s own structure ever being disturbed.

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Λ\Lambda

Symbol Lambda

completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state.

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ρ\rho

Symbol ρ

ρ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Λ(ρ)\Lambda(\rho)

Equation 17 · Evolutionary Physics

The Entry a Relabeling Cannot Write

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Λ†\Lambda^\dagger is positive because Λ\Lambda is completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state; it is unital, Λ†(Ic)\Lambda^\dagger(I_c) = IfI_f , because Λ\Lambda preserves trace for every input. This duality is the same construction Stinespring used to show that any completely positive map admits a dilation to a larger, unitary description [ 9 ] , and it lets a coarse Hamiltonian be pulled back onto the fine space without the fine space’s own structure ever being disturbed.

Meanings in this article

  • Λ\Lambda: completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state.
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