Entanglement and separable state

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phyky
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Entanglement is inseparable state |ψ>=[itex]\Sigma[/itex][itex]\Sigma[/itex]c(n1,n2)|n1n2> but for decoherence where system and environment coupling |ψ>(s,e)=[itex]\Sigma[/itex]c|s>[itex]\otimes[/itex]|e> which is normal tensor product, can we still say entanglement cause decoherece or just the tensor product between system and environment?
 
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Yes, entanglement is responsible for decoherence.