Common use of H H Clause in Contracts

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. In the binary case ( A and B both have dimension two), the above two conditions are equivalent and sufficient sufficient for the possibility of quantum key agree- mentagreement: all entangled binary states can be purifiedpurified. The same even holds if one Xxxxxxx space is of dimension 2 and the other one of dimension 3. HoweverHow- ever, 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 purified [17]. Such states are called bound entangled, in contrast to free entangled states, which can be purifiedpurified. Moreover, it is be- lieved believed that there even exist entangled states which cannot be purified purified although they have negative partial transposition [9].‌9].

H H. In the binary case ( A and B both have dimension two), the above two conditions are equivalent and sufficient sufficient for the possibility of quantum key agree- ment: all entangled binary states can be purifiedpurified. 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 purified [17]. Such states are called bound entangled, in contrast to free entangled states, which can be purifiedpurified. Moreover, it is be- lieved that there even exist entangled states which cannot be purified purified although they have negative partial transposition [9].‌