Bell Measurements and Observables

A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation are considered, and robustness of teleportation to various kinds of non idealities is shown.Comment: 11 pages. Elsart styl

Protocols for entanglement transformations of bipartite pure states

We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for ``pure contraction'' transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.Comment: 7 pages, no figures. Version slightly modified on Physical Review A reques

Prediction Validation of Two Glycaemic Control Models in Critical Care

Invited paperMetabolic models can substantially improve control of hyperglycaemia in critically ill patients. Control efficacy depends on how accurately a model-based system is able to predict future blood glucose (BG) concentrations after a glycaemic control intervention. This research compares two metabolic models in terms of their predictive power. 30 minutes to 10 hour forward predictions are made using the Glucosafe model (GS) and a clinically tested model (CC) from Christchurch in a retrospective study of 11 hyperglycemic patients, 6 from New Zealand and 5 from Denmark. Median and ranges of prediction errors are similar for predictions up to 360 minutes. Both models make better predictions on the Danish patients. At long prediction times of more than 5 hours, GS predictions tend to be more accurate in the cohort from New Zealand whereas the CC model tends to predict better in the cohort from Denmark. However, differences in root mean square (RMS) of prediction errors are not greater than 4–5% in both cohorts. For both models, outlying prediction errors are dominated by single patients, particularly type 1 diabetic patients. GS predicted BG values are generally higher compared to CC predicted values. As expected, the RMS prediction error increases with prediction interval for both models and cohorts. Results show the potential of both models for use in prospective clinical trials with longer than 120 min sampling intervals, though predictive power is probably related to the type of cohort in terms of admission type, degree of illness and glycaemic stability

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure

Three-body recombination rates near a Feshbach resonance within a two-channel contact interaction model

We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 22.7. The reduction is larger for larger effective ranges or, correspondingly, for narrower Feshbach resonances.Comment: 9 pages, 7 figure

Experimentally feasible measures of distance between quantum operations

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.Comment: 9 pages, 4 figure

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance

A quantum gate array can be programmed to evaluate the expectation value of any operator

A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|\Psi(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.Comment: 4 pages, 3 figures include

A Comprehensive Review on Renewable Energy Development, Challenges, and Policies of leading Indian States with an International Perspective

Clean and environment-friendly energy harvesting are of prime interest today as it is one of the key enablers in achieving the Sustainable Development Goals (SDGs) as well as accelerates social progress and enhances living standards. India, the second-most populous nation with a population of 1.353 billion, is one of the largest consumers of fossil fuels in the world which is responsible for global warming. An ever-increasing population is projected until 2050, and consequently, the energy demand in the upcoming decades will be co-accelerated by the rapid industrial growth. The Ministry of New and Renewable Energy (MNRE) with the support of National Institution for Transforming India (NITI) Aayog is working to achieve the Indian Government's target of attaining 175 GW through renewable energy resources. Many Indian states are currently increasing their renewable energy capacity in an objective to meet future energy demand. The review paper discusses in-depth about the three Indian states, namely Karnataka, Gujarat, Tamil Nadu, which pioneers the renewable energy production in India. The global energy scenario was discussed in detail with Indian contrast. Further, the barriers to the development of renewable energy generation and policies of the Indian government are discussed in detail to promote renewable energy generation throughout India as well as globally since the challenges are similar for other nations. This study analyzed various prospects of the country in renewable energy which has been done in a purpose to help the scholars, researchers, and policymakers of the nation, as it gives an insight into the present renewable energy scenario of the country.publishedVersio

Optimal estimation of qubit states with continuous time measurements

We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given $n$ identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large $n$, the statistical model described by $n$ identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term `local' refers to a shrinking neighborhood around a fixed state $\rho_{0}$. An essential result is that the neighborhood radius can be chosen arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by which we first localize the state within a smaller neighborhood of radius $n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy