arXiv subjects

Saptarshi Roy

Publications and source records attributed to Saptarshi Roy.

At least 37 records · Page 2Linked to original sources

arXiv2024

Feature Selection from Differentially Private Correlations

Data scientists often seek to identify the most important features in high-dimensional datasets. This can be done through $L_1$-regularized regression, but this can become inefficient for very high-dimensional datasets. Additionally, high-dimensional regression can leak information about individual datapoints in a dataset. In this paper, we empirically evaluate the established baseline method for feature selection with differential privacy, the two-stage selection technique, and show that it is not stable under sparsity. This makes it perform poorly on real-world datasets, so we consider a different approach to private feature selection. We employ a correlations-based order statistic to choose important features from a dataset and privatize them to ensure that the results do not leak information about individual datapoints. We find that our method significantly outperforms the established baseline for private feature selection on many datasets.

cs.LG↗

arXiv2024

Robustness of Higher Dimensional Nonlocality against dual noise and sequential measurements

Robustness in the violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality is investigated from the dual perspective of noise in measurements as well as in states. To quantify it, we introduce a quantity called the area of nonlocal region which reveals a dimensional advantage. Specifically, we report that with the increase of dimension, the maximally violating states show a greater enhancement in the area of nonlocal region in comparison to the maximally entangled states and the scaling of the increment, in this case, grows faster than visibility. Moreover, we examine the robustness in the sequential violation of CGLMP inequality using weak measurements and find that even for higher dimensions, two observers showing a simultaneous violation of the CGLMP inequality as obtained for two-qubit states persists. We notice that the complementarity between information gain and disturbance by measurements is manifested by the decrease of the visibility in the first round and the increase of the same in the second round with dimensions. Furthermore, the amount of white noise that can be added to a maximally entangled state so that it gives two rounds of the violation, decreases with the dimension, while the same does not appreciably change for the maximally violating states.

quant-ph↗

arXiv2024

Typical behaviour of genuine multimode entanglement of pure Gaussian states

Trends of genuine entanglement in Haar uniformly generated multimode pure Gaussian states with fixed average energy per mode are explored. A distance-based metric known as the generalized geometric measure (GGM) is used to quantify genuine entanglement. The GGM of a state is defined as its minimum distance from the set of all non-genuinely entangled states. To begin with, we derive an expression for the Haar averaged value of any function defined on the set of energy-constrained states. Subsequently, we investigate states with a large number of modes and provide a closed-form expression for the Haar averaged GGM in terms of the average energy per mode. Furthermore, we demonstrate that typical states closely approximate their Haar averaged GGM value, with deviation probabilities bounded by an exponentially suppressed limit. We then analyze the GGM content of typical states with a finite number of modes and present the distribution of GGM. Our findings indicate that as the number of modes increases, the distribution shifts towards higher entanglement values and becomes more concentrated. We quantify these features by computing the Haar averaged GGM and the standard deviation of the GGM distribution, revealing that the former increases while the latter decreases with the number of modes.

quant-ph↗

arXiv2024

Quantum illumination with noisy probes: Conditional advantages of non-Gaussianity

Entangled states, like the two-mode squeezed vacuum state, are known to give quantum advantage in the illumination protocol, a method to detect a weakly reflecting target submerged in a thermal background. We use non-Gaussian photon-added and -subtracted states, affected by local Gaussian noise on top of the omnipresent thermal noise, as probes in the illumination protocol. Based on the difference between the Chernoff bounds obtained with the coherent state and the non-Gaussian state having equal signal strengths, whose positive values denote quantum advantage in illumination, we highlight the hierarchy among non-Gaussian states, which is compatible with correlations per unit signal strength, although the Gaussian states offer the best performance. Interestingly, such hierarchy is different when comparisons are made using the Chernoff bounds. The entire analysis is performed in the presence of different imperfect apparatus like faulty twin-beam generator, imperfect photon addition (subtraction) as well as with noisy non-Gaussian probe states.

quant-ph↗

arXiv2024

Operational Ergotropy: suboptimality of the geodesic drive

We put forth a notion of optimality for extracting ergotropic work, derived from an energy constraint governing the necessary dynamics for work extraction in a quantum system. Within the traditional ergotropy framework, which predicts an infinite set of equivalent pacifying unitaries, we demonstrate that the optimal choice lies in driving along the geodesic connecting a given state to its corresponding passive state. Moreover, in a practical scenario where unitaries are inevitably affected by environmental factors, we refine the existing definition of ergotropy and introduce the notion of operational ergotropy. It enables the characterization of work extraction in noisy scenarios. We find that for certain typical noise models, the optimal choice which governs the Schrodinger part of the dynamics, aligns with the optimal drive in the unperturbed scenario. However, we demonstrate that such optimality is not universal by presenting an explicit counterexample. Additionally, within this generalized framework, we discuss the potential for faster work extraction from quantum systems in the presence of noise.

quant-ph↗

arXiv2023

Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.

stat.ME↗

arXiv2023

Emergence of Monogamy under Static and Dynamic Scenarios

Characterizing multipartite quantum correlations beyond two parties is of utmost importance for building cutting edge quantum technologies, although the comprehensive picture is still missing. Here we investigate quantum correlations (QCs) present in a multipartite system by exploring connections between monogamy score (MS), localizable quantum correlations (LQC), and genuine multipartite entanglement (GME) content of the state. We find that the frequency distribution of GME for Dicke states with higher excitations resembles that of random states. We show that there is a critical value of GME beyond which all states become monogamous and it is investigated by considering different powers of MS which provide various layers of monogamy relations. Interestingly, such a relation between LQC and MS as well as GME does not hold. States having a very low GME (low monogamy score, both positive and negative) can localize a high amount of QCs in two parties. We also provide an upper bound to the sum of bipartite QC measures including LQC for random states and establish a gap between the actual upper bound and the algebraic maximum.

quant-ph↗

arXiv2023

High-dimensional variable selection with heterogeneous signals: A precise asymptotic perspective

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and signal sparsity, we fix the minimum signal magnitude at the information-theoretic optimal rate and investigate the asymptotic selection accuracy of best subset selection (BSS) and marginal screening (MS) procedures. We show that despite the ideal setup, somewhat surprisingly, marginal screening can fail to achieve exact recovery with probability converging to one in the presence of heterogeneous signals, whereas BSS enjoys model consistency whenever the minimum signal strength is above the information-theoretic threshold. To mitigate the computational intractability of BSS, we also propose an efficient two-stage algorithmic framework called ETS (Estimate Then Screen) comprised of an estimation step and gradient coordinate screening step, and under the same scaling assumption on sample size and sparsity, we show that ETS achieves model consistency under the same information-theoretic optimal requirement on the minimum signal strength as BSS. Finally, we present a simulation study comparing ETS with LASSO and marginal screening. The numerical results agree with our asymptotic theory even for realistic values of the sample size, dimension and sparsity.

math.ST↗

arXiv2023

On Consistency and Asymptotic Normality of Least Absolute Deviation Estimators for 2-dimensional Sinusoidal Model

Estimation of the parameters of a 2-dimensional sinusoidal model is a fundamental problem in digital signal processing and time series analysis. In this paper, we propose a robust least absolute deviation (LAD) estimators for parameter estimation. The proposed methodology provides a robust alternative to non-robust estimation techniques like the least squares estimators, in situations where outliers are present in the data or in the presence of heavy tailed noise. We study important asymptotic properties of the LAD estimators and establish the strong consistency and asymptotic normality of the LAD estimators of the signal parameters of a 2-dimensional sinusoidal model. We further illustrate the advantage of using LAD estimators over least squares estimators through extensive simulation studies. Data analysis of a 2-dimensional texture data indicates practical applicability of the proposed LAD approach.

math.ST↗

arXiv2023

Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

stat.ML↗

arXiv2022

Quantum Dense Coding Network using Multimode Squeezed States of Light

We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states respectively. The dense coding capacity is calculated with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both the cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver.

quant-ph↗

arXiv2022

Significance of Fidelity Deviation in Continuous Variable Teleportation

Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in CV teleportation, i.e., the fidelity deviation as the figures of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios - one is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again lead to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one which leads to a `constructive effect' and identify the noise models which are responsible for decreasing average fidelity and increment in fidelity deviation.

quant-ph↗

arXiv2022

Quantum networks boosted by entanglement with a control system

Networks of quantum devices with coherent control over their configuration offer promising advantages in quantum information processing. So far, the investigation of these advantages assumed that the control system was initially uncorrelated with the data processed by the network. Here, we explore the power of quantum correlations between data and control, showing two communication tasks that can be accomplished with information-erasing channels if and only if the sender shares prior entanglement with a third party (the ``controller'') controlling the network configuration. The first task is to transmit classical messages without leaking information to the controller. The second task is to establish bipartite entanglement with a receiver, or, more generally, to establish multipartite entanglement with a number of spatially separated receivers.

quant-ph↗

arXiv2022

How does overparametrization affect performance on minority groups?

The benefits of overparameterization for the overall performance of modern machine learning (ML) models are well known. However, the effect of overparameterization at a more granular level of data subgroups is less understood. Recent empirical studies demonstrate encouraging results: (i) when groups are not known, overparameterized models trained with empirical risk minimization (ERM) perform better on minority groups; (ii) when groups are known, ERM on data subsampled to equalize group sizes yields state-of-the-art worst-group-accuracy in the overparameterized regime. In this paper, we complement these empirical studies with a theoretical investigation of the risk of overparameterized random feature models on minority groups. In a setting in which the regression functions for the majority and minority groups are different, we show that overparameterization always improves minority group performance.

cs.LG↗

arXiv2022

Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements

Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.

quant-ph↗

arXiv2022

Gain in Performance of Teleportation with Uniformity-breaking Distributions

Prior information about the input state can be utilized to enhance the efficiency of quantum teleportation which we quantify using the first two moments of fidelity. The input knowledge is introduced by relaxing the uniformity assumption in the distribution of the input state and considering non-uniform distributions, namely the polar cap and von Mises-Fisher densities. For these distributions,we show that the average fidelity increases while the deviation decreases with the increase of information content about the input ensemble thereby establishing its role as a resource. Our comparative study between these two distributions reveals that for the same amount of information content about inputs, although the average fidelity yield is the same for both, the polar cap distribution is "better" as it offers a smaller deviation. Moreover, we contrast the resource of prior information with other resources involved in the protocol like shared entanglement and classical communication. Specifically, we observe that unlike uniform distribution, the amount of classical communication required to fulfill the task decreases with the increase of information available for inputs. We also investigate the role of prior information in higher (three) dimensional teleportation and report the signatures of dimensional advantage in prior information-based teleportation.

quant-ph↗

arXiv2021

Distribution of entanglement with variable range interactions

Distribution of quantum entanglement is investigated for an anisotropic quantum XY model with variable range interactions and in the presence of a uniform transverse magnetic field. We report the possibility of \emph{qualitative} growth in the entanglement between distant sites with an increase in the range of interactions that vary either exponentially or polynomially as the distance between the sites increases. Interestingly, we find that such entanglement enhancement is not ubiquitous and is dependent on the factorization points, a specific set of system parameters where the zero-temperature state of the system is fully separable. In particular, we observe that at zero-temperature, when the system parameters are chosen beyond the pair of factorization points, the increments in entanglement length due to variable range interactions are more pronounced compared to the situation when the parameters lie in between the factorization points. By employing the sum of all the bipartite entanglements with respect to a single site, we also show that the shareability of the bipartite entanglements are constrained, thereby establishing their monogamous nature. Furthermore, we note that the factorization points get reallocated depending on the laws of interaction fall-offs and provide an ansatz for the same. We reveal that the temperature at which the canonical equilibrium state becomes entangled from an unentangled one increases with the increase in the range of interactions, thereby demonstrating enhanced robustness in entanglement against temperature in the presence of long-range interactions and only when the system parameters are chosen between the pair of factorization points. We apply an energy-based entanglement witness to provide a justification to the observed robustness with temperature.

quant-ph↗

arXiv2021

Quantum illumination with a light absorbing target

In a quantum illumination (QI) protocol, the task is to detect the presence of the target which is typically modelled by a partially reflecting beam splitter. We analyze the performance of QI when the target absorbs part of the light that falls on it, thereby making the scenario more realistic. We present an optical setup that models a target with these characteristics and explore its detectability in the quantum domain in terms of the Chernoff bound (CB). For an idler-free setup, we use the coherent state for QI while the two mode squeezed vacuum (TMSV) state is employed in the signal-idler scheme. In both the cases, we report an absorption-induced enhancement of the detection efficiency indicated by a lowering of CB with increasing amounts of absorption. Interestingly, we show that in the presence of absorption, a more intense thermal background can lead to target detection with enhanced efficiency. Moreover, we observe that the quantum advantage persists even for finite amounts of absorption. However, we find that the quantum advantage offered by TMSV decreases monotonically with absorption, and becomes vanishingly small in the high absorption regime. We also demonstrate the optimality of both the coherent and the TMSV states in their respective setups (idler-free and signal-idler) in the limit of low reflectivity and absorption.

quant-ph↗