H H. In the binary case ( A and B both have dimension two), the above two conditions are equivalent and sufficient for the possibility of quantum key agree- ment: all entangled binary states can be purified. The same even holds if one Xxxxxxx space is of dimension 2 and the other one of dimension 3. However, for larger dimensions there are examples showing that these conditions are not equivalent: There are entangled states whose partial transpose has no negative eigenvalue, hence cannot be purified [17]. Such states are called bound entangled, in contrast to free entangled states, which can be purified. Moreover, it is be- lieved that there even exist entangled states which cannot be purified although they have negative partial transposition [9].
H H. If the set of bases is large enough, then for all z there is a basis with posi- tive intrinsic information, hence the mean is also positive. Clearly, this result is stronger if the set of bases is small. Nothing is proven about the achievable size of such sets of bases, but it is conceivable that max dim A, dim B bases are always sufficient.
H H. – Commitment. From Lemma 2, all honest parties that complete AVSS-Sh would agree on the same h and c. According to the collision-resistance of hash function, the adversary cannot find a Cj = C such that h = (Cj) = (C ) with all but negligible probability, so there is a fixed C except with negligible probability. Moreover, C is computationally binding conditioned on DLog assumption, so all honest parties agree on the same polynomial A∗(x) committed to C , which fixes a unique key∗, and they also receive the same cipher c. So there exists a unique m∗ = c key∗, which can be fixed once some honest party outputs in AVSS-Sh. Now we prove that m∗ can be reconstructed when all honest parties activate AVSS-Rec. Any honest party outputs in the AVSS-Sh subprotocol must receive 2f + 1 Ready messages from distinct parties, at least f + 1 of which are from honest parties. Thus, at least one honest party has received 2f + 1 Echo messages from distinct parties. This ensures that at least f + 1 honest parties get the same commitment C and a valid quorum proof Π. Due the unforgeability of signatures in Π, that means at least f +1 honest parties did store valid shares of A∗(x) and B∗(x) along with the corresponding commitment C except with negligible probability. So after all honest parties start AVSS-Rec, there are at least f + 1 honest parties would broadcast KeyRec messages with valid shares of A∗(x) and B∗(x). These messages can be received by all parties and can be verified by at least f + 1 honest parties who record C . With overwhelming probability, at least f + 1 parties can interpolate A∗(x) to compute A∗(0) as key and broadcast it, and all parties can receive at least f + 1 same key∗ and then output the same m∗ = c key∗ as they obtain the same ciphertext c from AVSS-Sh.
H H. We want to replicate this generically in a relative setting, i.
H H. This Agreement is the GNI Tripartite Agreement referred to in the Interconnection Agreement. It is agreed:
H H. In the binary case ( A and B both have dimension two), the above two conditions are equivalent and su cient for the possibility of quantum key agree- ment: all entangled binary states can be xxxx xx. The same even holds if one Xxxxxxx space is of dimension 2 and the other one of dimension 3. However, for larger dimensions there are examples showing that these conditions are not equivalent: There are entangled states whose partial transpose has no negative eigenvalue, hence cannot be xxxx xx [17]. Such states are called bound entangled, in contrast to free entangled states, which can be xxxx xx. Moreover, it is be- lieved that there even exist entangled states which cannot be xxxx xx although they have negative partial transposition [9].
H H. The optimal power allocation policy to (P1-full) is thus given by
H H t t −t = t* + 2
H H. I 2. The Plaintiff’s case is that the Agreement was varied by a I verbal agreement between the parties. The Defendant argued that verbal K in this case is whether there is a verbal agreement which varied the terms of K M 3. Under the Agreement, the terms of payment were stipulated as M follows:- O 30% deposit be paid after signing of the Agreement; O 65% be paid within 30 days after completion of the works; 5% being retention money.
H H. ⇒ H′ for H′′ = ({a}, ♮1)[]({b}, 1 ), but Can(H) = Now(H) ={{({a}, ♮1)}} { { } } {{ { } }} and Can(H′) = Now(H′) = ( b , 1 ) . We have vanish(H), but tang(H′). To get the action rules correct under structural equivalence, the executions like that of ( b , 1 ) from H′ must be disabled using preconditions in the action rules, since immediate multiactions have a priority over stochastic ones, hence, the choices are always resolved in favour of the former. In Table 3, we define the action and empty loop rules. In this table, (α, ρ), (β, χ) ∈ SL, (α, ♮l), (β, ♮m) ∈ IL and (α, κ) ∈ SIL. Further, E, F ∈ RegStatExpr, G, H ∈ {∅}, Γ′ ∈ NSfinL, I, J ∈ NIfinL \ {∅}, I′ ∈ NIfinL and Υ ∈ NSfinIL \ {∅}. The first OpRegDynExpr, G˜, H˜ ∈ RegDynExpr and a ∈ Act. Moreover, Γ, ∆ ∈ NSfinL \ rule is the empty loop rule El. The other rules are the action rules, describing transformations of dynamic expressions, which are built using particular algebraic operations. If we cannot merge a rule with stochastic multiactions and a rule with immediate multiactions for some operation then we get the coupled action rules. Then the names of the action rules with immediate multiactions have a suffix “ i”. ≈ Almost all the rules in Table 3 (excepting El, P2, P2i, Sy2 and Sy2i) resemble those of gsPBC [60], but the former correspond to execution of sets of activities, not of single activities, as in the latter, and our rules have simpler preconditions (if any), since all immediate multiactions in dtsiPBC have the same priority level, unlike those of gsPBC. The preconditions in rules El, C, P1, I2 and I3 are needed to ensure that (possibly empty) sets of stochastic multiactions are executed only from tangible operative dynamic expressions, such that all operative dynamic expressions structurally equivalent to them are tangible as well. For example, if init(G) in rule C then G = F for some static expression F and G[]E = F []E F []E. Hence, it should be guaranteed that tang(F []E), which holds iff tang(E). The case E[]G is treated similarly. Further, in rule P1, assuming that tang(G), it should be guaranteed that tang(G H) and tang(H G), which holds iff tang(H). The preconditions in rules I2 and I3 are analogous to that in rule C. Rule El corresponds to one discrete time unit delay while executing no activities and therefore it has no analogues among the rules of gsPBC that adopts the continuous time model. Rules P2 and P2i have no similar rules in gsPBC, since interleaving semantics of the alge...
