Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation reveals that cloning converges to state discrimination followed by state preparation as the number of clones goes to infinity. The convergence exhibits a phenomenon analogous to a second-order symmetry-breaking phase transition.

Probabilistic metrology attains macroscopic cloning of quantum clocks.

It has recently been shown that probabilistic protocols based on postselection boost the performances of the replication of quantum clocks and phase estimation. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and state estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metrology can simulate cloning in the macroscopic limit for arbitrary sets of states when the performance of the simulation is measured by testing small groups of clones.

Quantum metrology assisted by abstention.

The main goal of quantum metrology is to obtain accurate values of physical parameters using quantum probes. In this context, we show that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically improve the measurement precision and even lead to a change in its asymptotic behavior, from the shot-noise to the Heisenberg scaling. We focus on phase estimation and quantify the required amount of abstention for a given precision. We also develop analytical tools to obtain the asymptotic behavior of the precision and required rate of abstention for arbitrary pure states.

Quantum learning without quantum memory.

A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required classical memory grows only logarithmically with the number of training qubits, while its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an "estimate-and-discriminate" machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.

Local discrimination of mixed States.

We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by local operations assisted with classical communication (LOCC). In contrast with the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former can require up to twice the number of copies of the latter. Our techniques can be used to bound the power of LOCC strategies in other similar settings, which is still one of the most elusive questions in quantum communication.

Discriminating States: the quantum Chernoff bound.

We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.

Separable measurement estimation of density matrices and its fidelity gap with collective protocols.

We show that there exists a gap between the performance of separable and collective measurements in the qubit mixed-state estimation that persists in the large sample limit. We characterize the gap with sharp asymptotic bounds on mean fidelity. We present an adaptive protocol that attains the separable measurement bound. This protocol uses von Neumann measurements and can be easily implemented with current technology.

Purity estimation with separable measurements.

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum memories provide no advantage in this situation. The relationship between our global Bayesian approach and the quantum Cramér-Rao bound is discussed.

Optimal scheme for estimating a pure qubit state via local measurements.

We present the optimal scheme for estimating a pure qubit state by means of local measurements on N identical copies. We give explicit examples for low N. For large N, we show that the fidelity saturates the collective measurement bound up to order 1/N. When the signal state lays on a meridian of the Bloch sphere, we show that this can be achieved without classical communication.

Aligning reference frames with quantum states.

We analyze the problem of sending, in a single transmission, the information required to specify an orthogonal trihedron or reference frame through a quantum channel made out of N elementary spins. We analytically obtain the optimal strategy, i.e., the best encoding state and the best measurement. For large N, we show that the average error goes to zero linearly in 1/N. Finally, we discuss the construction of finite optimal measurements.

Optimal strategies for sending information through A quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Structural alterations that differentially affect the mutagenic and antitrichomonal activities of 5-nitroimidazoles.

Two approaches have been used to develop nonmutagenic 5-nitroimidazoles. Both approaches are based on knowledge of the likely mechanisms by which this class of compounds cause mutagenicity. The first approach involved incorporating readily oxidizable gallate derivatives into the molecule. In one case, a very weakly mutagenic active antitrichomonal agent was obtained. The second approach involved incorporating a substituent at the C4 position of the ring. This generally resulted in a large reduction in mutagenicity and a lowering of antitrichomonal activity in vitro. In certain cases, however, mutagenicity was dramatically reduced while moderate antitrichomonal activity was retained. For example, 1,2-dimethyl-4-(2-hydroxyethyl)-5-nitroimidazole (5) showed good antitrichomonal activity in vitro (ED50 = 2 micrograms/kg) while possessing only 4% of the mutagenicity of metronidazole.

Tumorigenicity of nitrated derivatives of pyrene, benz[a]anthracene, chrysene and benzo[a]pyrene in the newborn mouse assay.

Eight nitropolycyclic aromatic hydrocarbons (PAHs), including 1- and 4-nitropyrene, 1,3-, 1,6- and 1,8-dinitropyrene, 7-nitrobenz[a]anthracene, 6-nitrochrysene and 6-nitrobenzo-[a]pyrene and their parent PAHs were tested fro tumorigenicity in the newborn mouse model by i.p. administration at 1, 8, and 15 days after birth. Both pyrene and 1-nitropyrene induced similar incidences of hepatic tumors in males, yielding a 12-15% and a 21-28% tumor incidence at total doses of 700 and 2800 nmol per mouse, respectively. Liver tumors did not occur in females and the 3-10% lung tumor yield in both sexes was similar to that found in solvent-treated controls. The presumed proximate carcinogen, 1-nitrosopyrene, administered at 700 nmol per mouse, caused liver tumors in 45% of the males and in 9% of the females. 4-Nitropyrene was more tumorigenic than pyrene or 1-nitropyrene; at a dose of 2800 nmol, it induced liver tumors in 83% of the males and 7% of the females, with a lung tumor yield of 38 and 31%, respectively. Female mice treated with 200 nmol of 1,3-, 1,6- or 1,8-dinitropyrene did not develop liver tumors but the hepatic tumor incidence in males was 20, 32 and 16%, respectively, which was significantly greater than that found in mice treated with pyrene. In male mice administered 2800 nmol of benz[a]anthracene, the hepatic tumor incidence was 79%, while treatment with 7-nitrobenz[a]anthracene showed an incidence of only 28%. Similarly, 560 nmol of benzo[a]pyrene caused a 49% liver tumor yield in males while those given 6-nitrobenzo[a]pyrene had a 28% incidence. Treatment with benzo[a]pyrene also induced a 35 and 48% lung tumor incidence in males and females while the comparable values in 6-nitrobenzo[a]pyrene-treated mice were 14 and 2%. Chrysene administered at 2800 nmol per mouse induced hepatic and lung tumors in 41% and 21% of the males, respectively; at the 700-nmol dose, it induced only liver tumors in 29% of the males and in none of the females. In contrast, treatment with 6-nitrochrysene at 700 nmol per mouse resulted in a 76 and 23% hepatic tumor incidence in males and females, respectively.(ABSTRACT TRUNCATED AT 400 WORDS)

Studies on the mechanism of activation and the mutagenicity of ronidazole, a 5-nitroimidazole.

Substantial evidence implicates the obligatory nucleophilic attack by water at C4 for the elimination of the carbamate and subsequent immobilization by electrophilic attack on protein thiols. Consequently, the strong correlation between the structural requirements for protein alkylation and for mutagenicity in TA100 suggests a possible role of nucleophilic addition at C4 or at the 2-methylene carbon for the expression of mutagenicity. Further studies directed at evaluating this possibility are currently in progress.

Drug residue formation from ronidazole, a 5-nitroimidazole. V. Cysteine adducts formed upon reduction of ronidazole by dithionite or rat liver enzymes in the presence of cysteine.

When ronidazole (1-methyl-5-nitroimidazole-2-methanol carbamate) is reduced by either dithionite or rat liver microsomal enzymes in the presence of cysteine, ronidazole-cysteine adducts can be isolated. Upon reduction with dithionite ronidazole can react with either one or two molecules of cysteine to yield either a monosubstituted ronidazole-cysteine adduct substituted at the 4-position or a disubstituted ronidazole-cysteine adduct substituted at both the 4-position and the 2-methylene position. In both products the carbamoyl group of ronidazole has been lost. The use of rat liver microsomes to reduce ronidazole led to the formation of the disubstituted ronidazole-cysteine adduct. These data indicate that upon the reduction of ronidazole one or more reactive species can be formed which can bind covalently to cysteine. The proposed reactive intermediates formed under these conditions may account for the observed binding of ronidazole to microsomal protein and the presence of intractable drug residues in the tissues of animals treated with this compound. They may also account for the mutagenicity of this compound in bacteria.

Drug residue formation from ronidazole, a 5-nitroimidazole. VI. Lack of mutagenic activity of reduced metabolites and derivatives of ronidazole.

The potential toxicity of ronidazole residues present in the tissues of food-producing animals was assessed using the Ames mutagenicity test. Since ronidazole is activated by reduction, reduced derivatives of ronidazole and metabolites formed by enzymatic reduction of ronidazole were tested for mutagenicity. When tested at levels several orders of magnitude higher than that at which ronidazole was mutagenic, 5-amino-4-S-cysteinyl-1,2- dimethylimidazole , a product of the dithionite reduction of ronidazole in the presence of cysteine, the 5-N-acetylamino derivative of ronidazole and 5-amino-1,2- dimethylimidazole all lacked mutagenic activity in Ames strain TA100. The metabolites of ronidazole formed by the incubation of ronidazole with microsomes under anaerobic conditions were also not mutagenic. These data demonstrate that although ronidazole is a potent mutagen, residues from it which may be present in the tissues of food-producing animals lack any mutagenic activity.

p-Toluenesulfonic acid/methanol: mild reagent for the preparation of bile acid methyl esters.

An improved method for the preparation of bile acid methyl esters is described. This is achieved by the addition of catalytic amounts of p-toluenesulfonic acid in a solution of bile acid in methanol. Advantages of this procedure over conventional methods include (1) use of a mild solid acid catalyst which prevents the formation of undesirable byproducts, (2) isolation of a solid product of high purity and (3) utilization of a relatively safe reagent in comparison to other methods involving diazomethane, hydrochloric acid or sulfuric acid.