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We use quantum discord to characterize the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys.
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The eigendecomposition ρ S M = ∑ a p a Π a \rho_{SM}=\sum_{a}p_{a}\Pi_{a} yields p j ρ S | j = ∑ a p a p j | a ρ S | a , j p_{j}\rho_{S|j}=\sum_{a}p_{a}p_{j|a}\rho_{S|a,j} , where ρ S | a , j = Tr M ( Π j Π a ) / p j | a \rho_{S|a,j}={\rm{Tr}}_{M}(\Pi_{j}\Pi_{a})/p_{j|a} is a pure state of S S . It follows from the pure-state decomposition ρ S | j = ∑ a p a | j ρ S | a , j \rho_{S|j}=\sum_{a}p_{a|j}\rho_{S|a,j} that H ( A | j ) ≥ S ( ρ S | j ) H(A|j)\geq S(\rho_{S|j}) . Thus H ( S , M ) = H ( A ) ≥ H ( A | J ) = ∑ j p j H ( A | j ) ≥ H ~ { Π j } ( S | M ) ≥ H ~ ( S | M ) H(S,M)=H(A)\geq H(A|J)=\sum_{j}p_{j}H(A|j)\geq\tilde{H}_{\{\Pi_{j}\}}(S|M)\geq\tilde{H}(S|M) , from which the upper bound on discord follows
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