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

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

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

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

Interval Bound Propagation\unicode{x2013}aided Few\unicode{x002d}shot Learning

Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks, from a given task distribution, to generalize to unseen tasks, from the same distribution, with a limited amount of labeled data. The underlying requirement for effective few-shot generalization is to learn a good representation of the task manifold. One way to encourage this is to preserve local neighborhoods in the feature space learned by the few-shot learner. To this end, we introduce the notion of interval bounds from the provably robust training literature to few-shot learning. The interval bounds are used to characterize neighborhoods around the training tasks. These neighborhoods can then be preserved by minimizing the distance between a task and its respective bounds. We further introduce a novel strategy to artificially form new tasks for training by interpolating between the available tasks and their respective interval bounds, to aid in cases with a scarcity of tasks. We apply our framework to both model-agnostic meta-learning as well as prototype-based metric-learning paradigms. The efficacy of our proposed approach is evident from the improved performance on several datasets from diverse domains in comparison to a sizable number of recent competitors

Anharmonicity can enhance the performance of quantum refrigerators

We explore a thermodynamical effect of anharmonicity in quantum mechanical oscillators. We show that small quartic perturbations to the oscillator potential lead to an enhancement of performance of quantum refrigerators for both the Otto and Stirling cycles. A similar nonlinearity driven enhancement of performance is also observed for an analogous spin-qubit model of quantum refrigerators. We further demonstrate the robustness of improvement of the coefficient of performance versus the energy cost for creating anharmonicity. It is shown that the anharmonicity driven improvement in performance is a generic effect at the quantum level for the experimentally realizable Otto refrigerator.Comment: 10 pages, 5 figure

Appropriateness of Performance Indices for Imbalanced Data Classification: An Analysis

Indices quantifying the performance of classifiers under class-imbalance, often suffer from distortions depending on the constitution of the test set or the class-specific classification accuracy, creating difficulties in assessing the merit of the classifier. We identify two fundamental conditions that a performance index must satisfy to be respectively resilient to altering number of testing instances from each class and the number of classes in the test set. In light of these conditions, under the effect of class imbalance, we theoretically analyze four indices commonly used for evaluating binary classifiers and five popular indices for multi-class classifiers. For indices violating any of the conditions, we also suggest remedial modification and normalization. We further investigate the capability of the indices to retain information about the classification performance over all the classes, even when the classifier exhibits extreme performance on some classes. Simulation studies are performed on high dimensional deep representations of subset of the ImageNet dataset using four state-of-the-art classifiers tailored for handling class imbalance. Finally, based on our theoretical findings and empirical evidence, we recommend the appropriate indices that should be used to evaluate the performance of classifiers in presence of class-imbalance.Comment: Published in Pattern Recognition (Elsevier