Common use of Let us Clause in Contracts

Let us. consider the so-called 4-state protocol of [3]. The analy- sis of the 6-state protocol [1] is analogous and leads to similar results [15]. We compare the possibility of quantum and classical key agreement given the quantum state and the corresponding classical distribution, respectively, arising from this protocol. The conclusion is, under the assumption of in- coherent eavesdropping, that key agreement in one setting is possible if and only if this is true also for the other. After carrying out the 4-state protocol, and under the assumption of op- timal eavesdropping (in terms of ▇▇▇▇▇▇▇ information), the resulting quan- tum state is [11] √ √ √ √ Ψ = F/2|0, 0)⊗ξ00+ D/2|0, 1)⊗ξ01+ D/2|1, 0)⊗ξ10+ F/2|1, 1)⊗ξ11 ∈ C2⊗C2⊗C4 , ƒ where D (the disturbance) is the probability that X = Y holds if X and Y are the classical random variables of ▇▇▇▇▇ and ▇▇▇, respectively, where F = 1 − D (the fidelity), and where the ξij satisfy (ξ00|ξ11) = (ξ01|ξ10) = 1 − 2D and (ξii|ξij) = 0 for all i ƒ= j. Then the state ρAB is (in the basis {| 00 ),| 01 ),| 10 ),| 11 )})  D 0 0 −D(1 − 2D)  ρAB 1  0 1 − D −(1 − D)(1 − 2D) 0  =  

Let us. consider the so-called 4-state protocol of [3]. The analy- sis of the 6-state protocol [1] is analogous and leads to similar results [15]. We compare the possibility of quantum and classical key agreement given the quantum state and the corresponding classical distribution, respectively, arising from this protocol. The conclusion is, under the assumption of in- coherent eavesdropping, that key agreement in one setting is possible if and only if this is true also for the other. After carrying out the 4-state protocol, and under the assumption of op- timal eavesdropping (in terms of ▇▇▇▇▇▇▇ information), the resulting quan- tum state is [11] √ √ √ √ Ψ = F/2|0, 0)⊗ξ000⟩⊗ξ00+ D/2|0, 1)⊗ξ011⟩⊗ξ01+ D/2|1, 0)⊗ξ100⟩⊗ξ10+ F/2|1, 1)⊗ξ11 1⟩⊗ξ11 ∈ C2⊗C2⊗C4 , ƒ / where D (the disturbance) is the probability that X = Y holds if X and Y are the classical random variables of ▇▇▇▇▇ and ▇▇▇, respectively, where F = 1 − D (the fidelity), and where the ξij satisfy (ξ00|ξ11) ⟨ξ00|ξ11⟩ = (ξ01|ξ10) ⟨ξ01|ξ10⟩ = 1 − 2D and (ξii|ξij) ⟨ξii|ξij⟩ = 0 for all i ƒ= /= j. Then the state ρAB is (in the basis {| 00 ),| ⟩,| 01 ),| ⟩,| 10 ),| ⟩,| 11 )⟩})  D 0 0 −D(1 − 2D)  ρAB 1  0 1 − D −(1 − D)(1 − 2D) 0  =  