Entanglement and Intrinsic Information. Let us first establish the connection between intrinsic information and entan- glement. Theorem 1 states that if ρAB is separable, then Eve can “force” the information between Alice’s and Bob’s classical random variables (given Eve’s classical random variable) to be zero (whatever strategy Xxxxx and Xxx use5). In particular, Eve can prevent classical key agreement. Theorem 1 Let Ψ ∈ HA ⊗HB ⊗HE and ρAB = TrHE (PΨ ). If ρAB is separable, then there exists a generating set {|z)} of HE such that for all bases {|x)} and {|y)} of HA2 |(x, y, z|Ψ)| . and HB, respectively, I(X; Y |Z) = 0 holds for PXY Z(x, y, z) := Proof. IfΣρAB is separable, then there exist vectors |αz) and |βz) such that z=1 z z
Entanglement and Intrinsic Information. Let us first establish the connection between intrinsic information and entan- glement. Theorem 1 states that if ρAB is separable, then Xxx can “force” the information between Xxxxx’s and Bob’s classical random variables (given Xxx’s classical random variable)to be zero (whatever strategy Xxxxx and Xxx use5). In particular, Xxx can prevent classical key agreement. Theorem 1 Let Ψ ∈ HA ⊗HB ⊗HE and ρAB = TrHE (PΨ ). If ρAB is separable, then there exists a generating set {|z⟩} of HE such that for all bases {|x⟩} and {|y⟩} of HA2 |⟨x, y, z|Ψ⟩| . and HB, respectively, I(X; Y |Z) = 0 holds for PXY Z(x, y, z) := Proof. IfΣρAB is separable, then there exist vectors |αz⟩ and |βz⟩ such that z=1 z z
Entanglement and Intrinsic Information. Let us rst establish the connection between intrinsic information and entan- glement. Theorem 1 states that if AB is separable, then Xxx can \force" the information between Xxxxx's and Xxx's classical random variables (given Xxx's classical random variable) to be zero (whatever strategy Xxxxx and Xxx use5). In particular, Xxx can prevent classical key agreement. Theorem 1 Let 2 HA HB HE and AB = TrHE (P ). If AB is separable, then there exists a generating set fjzig of HE such that for all bases fjxig and fjyig of HA and HB, respectively, I(X; Y jZ) = 0 holds for PXY Z(x; y; z) := jhx; y; zj ij .
Entanglement and Intrinsic Information. Let us first establish the connection between intrinsic information and entan- glement. Theorem 1 states that if ρAB is separable, then Eve can “force” the information between Alice’s and Bob’s classical random variables (given Eve’s classical random variable) to be zero (whatever strategy Xxxxx and Xxx use5). In particular, Eve can prevent classical key agreement. Theorem 1 Let Ψ ∈ HA ⊗ HB ⊗ HE and ρAB = TrHE (PΨ ). If ρAB is separable, then there exists a generating set {|z)} of HE such that for all bases {|x)} and {|y)} of HA and HB, respectively, I(X; Y |Z) = 0 holds for PXY Z(x, y, z) := |(x, y, z|Ψ )|2. 4 A priori, there is no privileged basis. However, physicists often write states like ρAB in a basis which seems to be more natural than others. We refer to this as the standard basis. Somewhat surprisingly, this basis is generally easy to identify, though not precisely defined. One could characterize the standard basis as the basis for which as many coefficients as possible of Ψ are real and positive. We usually represent quantum states with respect to the standard basis.
Entanglement and Intrinsic Information. Let us first establish the connection between intrinsic information and en- tanglement. Theorem 1 states that if ρAB is separable, then Xxx can “force” the information between Xxxxx’s and Bob’s classical random variables (given Xxx’s classical random variable) to be zero (whatever strategy Xxxxx and Xxx use). In particular, Xxx can prevent classical key agreement. Theorem 1 Let Ψ ∈ HA ⊗ HB ⊗ HE and ρAB = TrHE (PΨ). If ρAB is separable, then there exists a generating set {|z⟩} of HE such that for all bases {|x⟩} and {|y⟩} of HA and HB, respectively, I(X; Y |Z) = 0 holds for PXY Z(x, y, z) := |⟨x, y, z|Ψ⟩| .
