Entanglement transitions in random definite particle states

Entanglement within qubits are studied for the subspace of definite particle states or definite number of up spins. A transition from an algebraic decay of entanglement within two qubits with the total number $N$ of qubits, to an exponential one when the number of particles is increased from two to three is studied in detail. In particular the probability that the concurrence is non-zero is calculated using statistical methods and shown to agree with numerical simulations. Further entanglement within a block of $m$ qubits is studied using the log-negativity measure which indicates that a transition from algebraic to exponential decay occurs when the number of particles exceeds $m$. Several algebraic exponents for the decay of the log-negativity are analytically calculated. The transition is shown to be possibly connected with the changes in the density of states of the reduced density matrix, which has a divergence at the zero eigenvalue when the entanglement decays algebraically.Comment: Substantially added content (now 24 pages, 5 figures) with a discussion of the possible mechanism for the transition. One additional author in this version that is accepted for publication in Phys. Rev.

Record statistics in random vectors and quantum chaos

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records that is non-universal but tends to the Gumbel distribution asymptotically. The quantum standard map is used to study these statistics for the effect of correlations apart from normalization. It is seen that in the mixed phase space regime the number of intensity records is a power law in the dimensionality of the state as opposed to the logarithmic growth for random states.Comment: figures redrawn, discussion adde

Entanglement between two subsystems, the Wigner semicircle and extreme value statistics

The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when both subsystems have dimensions which are not too small and are of the same order. A simple random matrix model for the partial transpose is found to capture the entanglement properties well, including a transition across a critical dimension. Log-negativity is used to quantify entanglement between subsystems and analytic formulas for this are derived based on the simple model. The skewness of the eigenvalue density of $\rho_{12}^{T_2}$ is derived analytically, using the average of the third moment over the ensemble of random pure states. The third moment after partial transpose is also shown to be related to a generalization of the Kempe invariant. The smallest eigenvalue after partial transpose is found to follow the extreme value statistics of random matrices, namely the Tracy-Widom distribution. This distribution, with relevant parameters obtained from the model, is found to be useful in calculating the fraction of entangled states at critical dimensions. These results are tested in a quantum dynamical system of three coupled standard maps, where one finds that if the parameters represent a strongly chaotic system, the results are close to those of random states, although there are some systematic deviations at critical dimensions.Comment: Substantially improved version (now 43 pages, 10 figures) that is accepted for publication in Phys. Rev.

Assessment of seedling traits of rice landraces under different saline conditions

Salinity is one of the major abiotic stresses affecting rice growth and yield worldwide. In rice, the most critical stages which affect salinity at a greater level are germination, vegetative and reproductive stages.It is very important to know the genotypic variation among landraces under saline conditions at the seed germination stage to reduce the harmful effect of salinity. The present study conducted on Petri plate was mainly for assessing germination, relative water content and seedling parameters of eleven rice landraces with check landrace Pokali under three different salt concentrations (75mM, 125mM and 150mM). Two-way ANOVA gave the variations among the genotypes, treatments and their interactions. The present study showed that Mundan, Odiyan, Muttadan, Kallimadiyan and Vellimuthu had less percentage reduction in growth parameters at the germination stage. Odiyan and Mundan showed less percentage reduction in fresh weight (36.09%) and  shoot length (25.61%) respectively, in relative water content  (10.70% and 16.07%, respectively) at higher concentrations of salinity (150mM) compared to control. Pokali, Chembakam and Odiyan showed good germination parameters under three different saline treatments compared to other genotypes. Biplot analysis showed 65.4% variation between the treatments, whereas the variation between the genotypes was around 13.3%. Screening of landraces for salinity tolerance at the seed germination stage is the most reliable method to identify the salt tolerant line at the early seedling stage. The present study can be used for further screening programme at the vegetative stage for the identification of potential salt tolerant lines to improve breeding and gene introgression studies

Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum

We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the entanglement expected of fully randomized states in the opposite limit is governed by the single scaling transition parameter, $\Lambda$. The behaviors apply equally well to few- and many-body systems, e.g.\ interacting particles in quantum dots, spin chains, coupled quantum maps, and Floquet systems as long as their subsystems are quantum chaotic, and not localized in some manner. To calculate the generalized moments of the Schmidt eigenvalues in the perturbative regime, a regularized theory is applied, whose leading order behaviors depend on $\sqrt{\Lambda}$. The marginal case of the $1/2$ moment, which is related to the distance to closest maximally entangled state, is an exception having a $\sqrt{\Lambda}\ln \Lambda$ leading order and a logarithmic dependence on subsystem size. A recursive embedding of the regularized perturbation theory gives a simple exponential behavior for the von Neumann entropy and the Havrda-Charv{\' a}t-Tsallis entropies for increasing interaction strength, demonstrating a universal transition to nearly maximal entanglement. Moreover, the full probability densities of the Schmidt eigenvalues, i.e.\ the entanglement spectrum, show a transition from power laws and L\'evy distribution in the weakly interacting regime to random matrix results for the strongly interacting regime. The predicted behaviors are tested on a pair of weakly interacting kicked rotors, which follow the universal behaviors extremely well

AWARENESS, KNOWLEDGE AND ATTITUDE TOWARDS PHARMACOVIGILANCE AMONG MEDICAL GRADUATES IN A TERTIARY CARE TEACHING HOSPITAL IN SOUTH INDIA.

Objectives: As an ever growing scale people are using newer and more effective drugs for various medical conditions. Adverse drug reactions (ADRs) are preventable if the health-care professional pays close attention to the details of the adverse effects, following a drug administration. Awareness about ADRs can decrease the irrational use of drugs. Hence, there is an urgent need to create awareness among the prescribers about the ADR monitoring. Hence, this study is undertaken to assess the awareness, knowledge, and attitude toward Pharmacovigilance among the future health-care professionals.Methods: Questionnaire-based study was conducted in a tertiary health-care hospital after getting approval from the Institutional Ethical Committee. The questionnaire was developed to assess the knowledge, awareness, and practice of Pharmacovigilance activity. The questions were distributed to the final year students, interns, and postgraduate's students and allowed to write down the answers independently. Each correct answer was given a score of ‘1,' whereas the incorrect/incomplete was given a score of 0.â€Results and Conclusion: The study reported that awareness (UGs - 53.3%, interns - 54.9%, PGs - 30.75) was adequate among undergraduates and interns, in the knowledge part (UGs-65.5%, interns - 35.4%, PGs - 9.2%), undergraduates excel far than the interns and PGs. However, in the application of Pharmacovigilance (UG - 22.2%, interns - 59.8%, PGs - 63.1%) postgraduates and interns fair better than the undergraduates. Hence, there is need to increase the awareness and also increase the ADR reporting practice among medical graduates

Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field

We study a one-dimensional Ising model with a magnetic field and show that tilting the field induces a transition to quantum chaos. We explore the stationary states of this Hamiltonian to show the intimate connection between entanglement and avoided crossings. In general entanglement gets exchanged between the states undergoing an avoided crossing with an overall enhancement of multipartite entanglement at the closest point of approach, simultaneously accompanied by diminishing two-body entanglement as measured by concurrence. We find that both for stationary as well as nonstationary states, nonintegrability leads to a destruction of two-body correlations and distributes entanglement more globally.Comment: Corrections in two figure captions and one new reference. To appear in Phys. Rev.

Quantum chaos in the spectrum of operators used in Shor's algorithm

We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the CUE ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators, in particular it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps, and in toy models of the quantum bakers map.Comment: Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publication in Phys. Rev. E as Rapid Com