Quantum Bayes rule

We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.Comment: REVTEX, 9 page

Solvent extraction and lanthanide complexation studies with new terdentate ligands containing two 1,3,5-triazine moieties

The extracting agent 2,6-bis(4,6-di-pivaloylamino-1,3,5-triazin-2-yl)-pyridine (L-5) in n-octanol was found, in synergy with 2-bromodecanoic acid, to give D-Am/D-Eu separation factors (SFs) between 2.4 and 3.7 when used to extract the metal ions from 0.02-0.12 M HNO3. Slightly higher SFs (4-6) were obtained in the absence of the synergist when the ligand was used to extract Am(III) and Eu(III) from 0.98 M HNO3. In order to investigate the possible nature of the extracted species crystal structures of L-5 and the complex formed between Yb(III) with 2,6-bis(4,6-di-amino-1,3,5-triazin-2-yl)-pyridine (L-4) were also determined. The structure of L-5 shows 3 methanol solvent molecules all of which form 2 or 3 hydrogen bonds with triazine nitrogen atoms, amide nitrogen or oxygen atoms, or pyridine nitrogen atoms. However, L-5 is relatively unstable in metal complexation reactions and loses amide groups to form the parent tetramine L-4. The crystal structure of Yb(L-4)(NO3)(3) shows ytterbium in a 9-coordinate environment being bonded to three donor atoms of the ligand and three bidentate nitrate ions. The solvent extraction properties of L-4 and L-5 are far inferior to those found for the 2,6-bis-(1,2,4-triazin-3-yl)-pyridines (L-1) which have SF values of ca. 140 and theoretical calculations have been made to compare the electronic properties of the ligands. The electronic charge distribution in L-4 and L-5 is similar to that found in other terdentate ligands such as terpyridine which have equally poor extraction properties and suggests that the unique properties of L-1 evolve from the presence of two adjacent nitrogen atoms in the triazine rings

Separation of lanthanides and actinides(III) using tridentate benzimidazole, benzoxazole and benzothiazole ligands

The ability of new hydrophobic tridentate ligands based on 2,6-bis(benziinidazol-2-yl)pyridine, 2,6-bis(benzoxazol-2-yl)pyridine and 2,6-bis(benzothiazol-2-yl)pyridine to selectively extract americium(III) from europium(III) was measured. The most promising ligand-2,6-bis(benzoxazol-2-yl)-4-(2-decyl-1-tetradecyloxy)pyridine L-9 was found to give separation factors (SFAm/Eu) of up to 70 when used to extract cations from 0.02-0.10 M HNO3 into TPH in synergy with 2-bromodecanoic acid. Six structures of lanthanide complexes with 2,6-bis(benzoxazol-2-yl)pyridine L-6 were then determined to evaluate the types of species that are likely to be involved in the separation process. Three structural types were observed, namely [LnL(6)(NO3)(3)(H2O)2], 11-coordinate only for La, [LnL(6) (NO3)(3) (CH3CN)], 10-coordinate for Pr, Nd and Eu and [LnL(6) (NO3)(3)(H2O)], L 10-coordinate for Eu and Gd. Quantum Mechanics calculations were carried out on the tridentate ligands to elucidate the conformational preferences of the ligands in the free state and protonated and diprotonated forms and to assess the electronic properties of the ligands for comparison with other terdentate ligands used in lanthanide/actinide separation processes