Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

Fruit weight and shoot diameter relationship in early ripening peaches

Data were collected in early ripening peach [Prunus persica (L.) Batsch] varieties trained to a vase system to determine if a relationship exists between fruit weight and shoot diameter. The experiment was conducted with 3 varieties at Gainesville, FL with detailed pruning and with 3 other varieties at Atapulgus, GA with minimum pruning. All the varieties were similar in fruit development period (FDP) and fruit size. The largest shoot diameter was generally found in the upper canopy in all varieties. There was no correlation between shoot diameter and fruit weight for 'TropicBeauty', 'TropicSnow' and 'UF2000' at Gainesville under detailed pruning. There was a significant (p = 0.01) correlation for 'Flordacrest' in the lower (r = 0.53) canopy and for 'White Robin' in both the upper (r = 0.38) and lower (r = 0.40) canopy at Attapulgus, GA under minimal pruning. In these situations, large stems were associated with large fruit. 'Delta', grown at Attapulgus with minimal pruning, showed no correlation between shoot diameter and fruit weight, probably because it is male sterile and produced large fruit due to a reduced crop load.