Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine e.g. the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics and observables. Here we propose a more practical strategy, that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the dimension of the Hilbert space can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.Comment: v3: accepted version. We would like to offer our gratitudes to the editors and referees for their helpful and insightful opinions and feedback

Quantifying precision loss in local quantum thermometry via diagonal discord

When quantum information is spread over a system through nonclassical correlation, it makes retrieving information by local measurements difficult---making global measurement necessary for optimal parameter estimation. In this paper, we consider temperature estimation of a system in a Gibbs state and quantify the separation between the estimation performance of the global optimal measurement scheme and a greedy local measurement scheme by diagonal quantum discord. In a greedy local scheme, instead of global measurements, one performs sequential local measurement on subsystems, which is potentially enhanced by feed-forward communication. We show that, for finite-dimensional systems, diagonal discord quantifies the difference in the quantum Fisher information quantifying the precision limits for temperature estimation of these two schemes, and we analytically obtain the relation in the high-temperature limit. We further verify this result by employing the examples of spins with Heisenberg's interaction.Comment: 5+4 pages, 4 figures, We thank the referees and editors for helpful opinions. Accepted by Phys. Rev. A (accepted version

On the instability for the cubic nonlinear Schrodinger equation

We study the flow map associated to the cubic Schrodinger equation in space dimension at least three. We consider initial data of arbitrary size in $H^s$, where $0<s<s_c$, $s_c$ the critical index, and perturbations in H^\si, where \si is independent of $s$. We show an instability mechanism in some Sobolev spaces of order smaller than $s$. The analysis relies on two features of super-critical geometric optics: creation of oscillation, and ghost effect.Comment: 4 page

VALUE OF NEW TECHNOLOGIES IN DAIRY FARMING: THE CASE OF ROBOTIC MILKING

The economic value of the innovation robotic milking systems (AMS) is examined for Swedish dairy operations. A mixed integer mathematical programming model, considering crops, calving distribution, seasonality and capacity constraints of the AMS system, is developed. The marginal value of increasing the capacity of the AMS unit is found to amount to 40-60% of the milk revenues per cow.Technology innovations, Dairy systems, Livestock Production/Industries, Q12,

Comparative analysis of upper limb and lower limb exercise training along with conventional physiotherapy in improving FeV1 and vital capacity in COPD subjects

INTRODUCTION: Chronic obstructive pulmonary disease (COPD) is a major cause of morbidity, mortality, and health care use. Exercise intolerance is one of the most troubling manifestations of COPD. Chronic Obstructive Pulmonary Disease (COPD) is a chronic slowly progressive disorder characterized by airflow obstruction (reduced FEV1 and FEV1/VC ratio) that does not change markedly over several months. In India a median prevalence of 5 per cent in men and 2.7 per cent in women was calculated which accounted for a total burden of 8.15 million male and 4.21 million female patients in a population of 944.5 million in 1996. NEED OF STUDY 1. This study is aimed to find out effects of upper limb exercise training in improving FEV1 and vital capacity in COPD subjects. 2. This study is aimed to find out effects of lower limb exercise training in improving FEV1 and vital capacity in COPD subjects. 3. This study used to compare the upper limb and lower limb exercise training in improving FEV1 and vital capacity in COPD subjects. METHODOLOGY: Study Design: Pre test and post test Comparative study. Group A: lower limb exercise training group along with conventional physiotherapy. Group B:upper limb exercise training group along with conventional physiotherapy. Source of Data: MAGJ Hospital, Mookkannoor, Ernakulam. Kerala. Sample and Sampling Method: 20 subjects were selected and randomly assigned in to one of the two training groups. Inclusion criteria: COPD above 45 years-60 years, Both male and female, Patients with chronic bronchitis, Patient had air flow obstruction. (FEV, FEC is < 80%). Exclusion criteria: Patients with unstable cardiac disease, Acute rib fracture, Subject not able to do PFT. Patients with TB, Pneumonia, Carcinoma of lung, Psychiatric illness. RESULTS: The number of subjects for the study were 20 (n=20). The subjects were divided in to two groups. For one group A (10 subjects) upper limb exercise training was given and for other group B (10 subjects) lower limb exercise training was given. The subjects were given training for 2 months continuously. Before starting the training pretest value is measured. The measurement was repeated after the training (post test value). Reading pre and post test value of group A and B are given in table. Thus in both groups there was significant improvement scores of FEV1 and vital capacity. When analyzing the fev1values of group A, by paired ‘t’ test the calculated t value for is 94.88 and ‘t’ table value is 4.78 at 0.001 level. Since the calculated ‘t’ value is more than ‘t’ table value, it is concluded that there is significant difference in the pre and post test values of FEV1 following upper limb training among COPD subjects. CONCLUSION: Chronic obstructive pulmonary disease defined as a usually progressive with air flow limitation that is not fully reversible and that is associated with abnormal inflammatory response of the lungs to noxious particles or gases. Physical therapy combining breathing exercise, chest Physiotherapy, are used. This study projects that both upper limb and lower limb training are effective in the treatment options in COPD. When comparing the mean value of all the group, Group A which received upper limb training showed more difference than other two group which received lower limb training. Hence we can conclude that upper limb training are more effective than lower limb training in improving FeV1among COPD patients