Sharing of Non-Local Advantage of Quantum Coherence by sequential observers

Non-local Advantage of Quantum Coherence(NAQC) or steerability of local quantum coherence is a strong non-local resource based on coherence complementarity relations. In this work, we provide an upper bound on the number of observers who can independently steer the coherence of the observer in the other wing in a scenario where half of an entangled pair of spin-$\frac{1}{2}$ particles is shared between a single observer (Bob) in one wing and several observers (Alices) on the other, who can act sequentially and independently of each other. We consider one-parameter dichotomic POVMs for the Alices and mutually unbiased basis in which Bob measures coherence in case of the maximally entangled bipartite qubit state. We show that not more than two Alices can exhibit NAQC when $l_1$-norm of coherence measure is probed, whereas for two other measures of coherence, only one Alice can reveal NAQC within the same framework.Comment: 7 page

Clustering with Missing Features: A Penalized Dissimilarity Measure based approach

Many real-world clustering problems are plagued by incomplete data characterized by missing or absent features for some or all of the data instances. Traditional clustering methods cannot be directly applied to such data without preprocessing by imputation or marginalization techniques. In this article, we overcome this drawback by utilizing a penalized dissimilarity measure which we refer to as the Feature Weighted Penalty based Dissimilarity (FWPD). Using the FWPD measure, we modify the traditional k-means clustering algorithm and the standard hierarchical agglomerative clustering algorithms so as to make them directly applicable to datasets with missing features. We present time complexity analyses for these new techniques and also undertake a detailed theoretical analysis showing that the new FWPD based k-means algorithm converges to a local optimum within a finite number of iterations. We also present a detailed method for simulating random as well as feature dependent missingness. We report extensive experiments on various benchmark datasets for different types of missingness showing that the proposed clustering techniques have generally better results compared to some of the most well-known imputation methods which are commonly used to handle such incomplete data. We append a possible extension of the proposed dissimilarity measure to the case of absent features (where the unobserved features are known to be undefined)

Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness: An Evolutionary Multi-Objective Optimization Approach

Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents Entropy $c$-Means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multi-objective optimization methods, Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D). We also propose a method to select a suitable trade-off clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multi-objective methods for fuzzy clustering.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Boosting with Lexicographic Programming: Addressing Class Imbalance without Cost Tuning

A large amount of research effort has been dedicated to adapting boosting for imbalanced classification. However, boosting methods are yet to be satisfactorily immune to class imbalance, especially for multi-class problems. This is because most of the existing solutions for handling class imbalance rely on expensive cost set tuning for determining the proper level of compensation. We show that the assignment of weights to the component classifiers of a boosted ensemble can be thought of as a game of Tug of War between the classes in the margin space. We then demonstrate how this insight can be used to attain a good compromise between the rare and abundant classes without having to resort to cost set tuning, which has long been the norm for imbalanced classification. The solution is based on a lexicographic linear programming framework which requires two stages. Initially, class-specific component weight combinations are found so as to minimize a hinge loss individually for each of the classes. Subsequently, the final component weights are assigned so that the maximum deviation from the class-specific minimum loss values (obtained in the previous stage) is minimized. Hence, the proposal is not only restricted to two-class situations, but is also readily applicable to multi-class problems. Additionally,we also derive the dual formulation corresponding to the proposed framework. Experiments conducted on artificial and real-world imbalanced datasets as well as on challenging applications such as hyperspectral image classification and ImageNet classification establish the efficacy of the proposal.Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Protecting temporal correlations of two-qubit states using quantum channels with memory

Quantum temporal correlations exhibited by violations of Leggett-Garg Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to be non-increasing under decoherence channels when probed on two-qubit pure entangled states. We study the action of decoherence channels, such as amplitude damping, phase-damping and depolarising channels when partial memory is introduced in a way such that two consecutive uses of the channels are time-correlated. We show that temporal correlations demonstrated by violations of the above temporal inequalities can be protected against decoherence using the effect of memory.Comment: 12 pages, 8 figure

Preservation of quantum non-bilocal correlations in noisy entanglement-swapping experiments using weak measurements

A tripartite quantum network is said to be bilocal if two independent sources produce a pair of bipartite entangled states. Quantum non-bilocal correlation emerges when the central party which possesses two particles from two different sources performs Bell-state measurement on them and nonlocality is generated between the other two uncorrelated systems in this entanglement-swapping protocol. The interaction of such systems with the environment reduces quantum non-bilocal correlations. Here we show that the diminishing effect modelled by the amplitude damping channel can be slowed down by employing the technique of weak measurements and reversals. It is demonstrated that for a large range of parameters the quantum non-bilocal correlations are preserved against decoherence by taking into account the average success rate of the post-selection governing weak measurements.Comment: 12 pages, 16 figure

Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation

We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range for two qubit Werner states in the two measurement and two outcome scenario. We further employ the derived steering relation for several classes of continuous variable systems. We show that non-Gaussian entangled states such as the photon subtracted squeezed vacuum state and the two-dimensional harmonic oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous variable states

Preservation of quantum key rate in the presence of decoherence

It is well known that the interaction of quantum systems with the environment reduces the inherent quantum correlations. Under special circumstances the effect of decoherence can be reversed, for example, the interaction modeled by an amplitude damping channel can boost the teleportation fidelity from the classical to the quantum region for a bipartite quantum state. Here, we first show that this phenomena fails in the case of a quantum key distribution protocol. We further show that the technique of weak measurement can be used to slow down the process of decoherence, thereby helping to preserve the quantum key rate when one or both systems are interacting with the environment via an amplitude damping channel. Most interestingly, in certain cases weak measurement with post-selection where one considers both success and failure of the technique is shown to be more useful than without it when both systems interact with the environment.Comment: 7 Pages, 5 figures, Comments are welcom

Diversifying Support Vector Machines for Boosting using Kernel Perturbation: Applications to Class Imbalance and Small Disjuncts

The diversification (generating slightly varying separating discriminators) of Support Vector Machines (SVMs) for boosting has proven to be a challenge due to the strong learning nature of SVMs. Based on the insight that perturbing the SVM kernel may help in diversifying SVMs, we propose two kernel perturbation based boosting schemes where the kernel is modified in each round so as to increase the resolution of the kernel-induced Reimannian metric in the vicinity of the datapoints misclassified in the previous round. We propose a method for identifying the disjuncts in a dataset, dispelling the dependence on rule-based learning methods for identifying the disjuncts. We also present a new performance measure called Geometric Small Disjunct Index (GSDI) to quantify the performance on small disjuncts for balanced as well as class imbalanced datasets. Experimental comparison with a variety of state-of-the-art algorithms is carried out using the best classifiers of each type selected by a new approach inspired by multi-criteria decision making. The proposed method is found to outperform the contending state-of-the-art methods on different datasets (ranging from mildly imbalanced to highly imbalanced and characterized by varying number of disjuncts) in terms of three different performance indices (including the proposed GSDI).Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-Massar-Popescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-$1$ component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-$1$ component observables, QM violation of GWI is more robust for both the type of states considered.Comment: Published Versio