arXiv subjects

Saptarshi Roy

Publications and source records attributed to Saptarshi Roy.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement-enhanced fluctuation-free daemonic ergotropy with random measurements

Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.

quant-ph↗

arXiv2026

Optimal Self-Distillation for Rectified Flow via Linear Probing

Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of true RF velocities and teacher velocities provably improve the teacher? For linear RF with ridge regularization on fixed interpolation pairs, we prove an exact affine path identity, derive the optimal mixing coefficient in closed form, and show strict improvement in integrated velocity risk whenever the teacher risk is nonstationary along the regularization path. The optimal coefficient obeys a sign rule: positive mixing corrects under-regularized teachers, while negative mixing corrects over-regularized teachers. We also give one-shot generalized cross-validation (GCV) and validation tuning procedure that avoids grid search over mixing weights and repeated refitting. Combining this theorem with RF Wasserstein convergence bounds, we show that optimal self-distillation improves the velocity estimation terms controlling continuous-time and finite-step generation error. Experiments with Gaussian models, Gaussian mixtures, and image data show that optimal self-distillation improves velocity risk, mode recovery, and finite-step generation relative to both the teacher and pure distillation.

stat.ML↗

arXiv2026

Exploring the periodicity of flight patterns

Each year the American Statistical Association (ASA) hosts the Annual Data Challenge Expo, which tasks participants with analyzing a given dataset and presenting their work at the Joint Statistical Meeting (JSM). The 2025 Data Challenge Expo tasked participants with analyzing over 35 years of commercial flight data from the United States Bureau of Transportation Statistics (BTS). These data provide extensive geographic coverage and operational details for the U.S. domestic aviation market. For millions of past flights, there is information about the flight's date, origin, destination, carrier, plane, departure, and arrival. In this article, we present our analysis for the 2025 JSM Data Challenge Expo. We chose to explore patterns in the daily scheduling of departures and arrivals across airlines, airports, and time. In doing so, we observed distinct scheduling ``waves'', or periodic structures at major airline hubs as well as large Federal Aviation Administration (FAA) hubs. In the remainder of this article, we detail the process of visualizing periodicity in flight scheduling as well as quantifying it through the calculation of Shannon entropy. An additional element to the 2025 Data Challenge Expo is the incorporation of a second dataset, to be decided by the participants. We detail the use of a BTS dataset with passenger enplanement (boarding) information to determine Federal Aviation Administration (FAA) hub classification (as opposed to airline-specific hubs). Furthermore, we discuss results from this visual and quantitative analysis, highlighting noticeable differences in the scheduling periodicity and entropy across airports, for the ``big four'' or four largest carriers, in U.S. aviation: American Airlines, Delta Air Lines, United Airlines, and Southwest Airlines.

stat.AP↗

arXiv2026

Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers

We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems by quantifying the gap between globally and locally extractable work (ergotropy). For arbitrary pure multimode Gaussian states, we prove that the $2$-local ergotropic gap is a faithful entanglement monotone across any bipartition and constitutes a functionally independent upper bound to the Renyi-2 entanglement entropy. We further introduce the $k$-ergotropic score, the minimum $k$-local ergotropic gap, and show that it faithfully quantifies multimode entanglement across $k$ partitions. For pure three-mode Gaussian states, we derive its closed-form relation with the geometric measure for genuine multimode entanglement $(k=2)$, and total Gaussian multimode entanglement $(k=3)$. For systems with more than three modes, the $k$-ergotropic score becomes a functionally independent measure of multimode entanglement to the standard geometric measures. Our results reveal a direct operational hierarchy linking Gaussian multimode entanglement to work extraction under locality constraints, and provide a computable and experimentally accessible thermodynamic framework for characterizing quantum correlations.

quant-ph↗

arXiv2026

Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective

In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic low dimensionality of the support of the target distribution to accelerate sampling. We show that, using a carefully designed choice of the time-discretization scheme and with sufficiently accurate drift estimates, the RF sampler enjoys an iteration complexity of order $O(k/\varepsilon)$ (up to log factors), where $\varepsilon$ is the precision in total variation distance and $k$ is the intrinsic dimension of the target distribution. In addition, we show that the denoising diffusion probabilistic model (DDPM) procedure is equivalent to a stochastic version of RF by establishing a novel connection between these processes and stochastic localization. Building on this connection, we further design a stochastic RF sampler that also adapts to the low-dimensionality of the target distribution under milder requirements on the accuracy of the drift estimates, and also with a specific time schedule. We illustrate with simulations on the synthetic data and text-to-image data experiments the improved performance of the proposed samplers implementing the newly designed time-discretization schedules.

stat.ML↗

arXiv2025

Random access Bell game by sequentially measuring the control of the quantum SWITCH

Preserving quantum correlations such as Bell nonlocality in noisy environments remains a fundamental challenge for quantum technologies. We introduce the Random Access Bell Game (RABG), a task where an entangled particle propagates through a sequence of identical noisy blocks, and the ability to violate a Bell inequality is tested at a randomly chosen point (access node). We consider a scenario where each noisy block is composed of two complete erasure channels, an extreme entanglement-breaking channel with vanishing quantum and classical capacities. We investigate the performance of the Random Access Bell Game in this configuration and attempt to mitigate the effect of noise by coherently controlling the order of each channel in the noise using the quantum {\tt SWITCH}. However, the quantum {\tt SWITCH} in its canonical setup with a coherent state in the control fails to provide any advantage in the Random Access Bell Game. Our main contribution is a protocol that leverages initial entanglement between the target and control of the quantum {\tt SWITCH} and employs sequential, unsharp measurements on the control system, showing that it is possible to guarantee a Bell violation after an arbitrarily large number of channel applications. Furthermore, our protocol allows for a near-maximal (Tsirelson bound) Bell violation to be achieved at any desired round, while still ensuring violations in all preceding rounds. We prove that this advantage is specific to generalized Greenberger-Horne-Zeilinger (GHZ) states, as the protocol fails for W-class states, thus providing an operational way to distinguish between these two fundamental classes of multipartite entanglement.

quant-ph↗

arXiv2025

Classical capacities under physical constraints: More capacity with less entanglement

Current advancements in communication equipment demand the investigation of classical information transfer over quantum channels, by encompassing realistic scenarios in finite dimensions. To address this issue, we develop a framework for analyzing classical capacities of quantum channels where the set of states used for encoding information is restricted based on various physical properties. Specifically, we provide expressions for the classical capacities of noiseless and noisy quantum channels when the average energy of the encoded ensemble or the energy of each of the constituent states in the ensemble is bounded. In the case of qubit energy-preserving dephasing channels, we demonstrate that a nonuniform probability distribution based on the energy constraint maximizes capacity, while we derive the compact form of the capacity for equiprobable messages. We suggest an energy-constrained dense coding (DC) protocol that we prove to be optimal in the two-qubit situation and obtain a closed-form expression for the DC capacity. Additionally, we demonstrate a no-go result, which states that when the dimension of the sender and the receiver is two, no energy-preserving operation can offer any quantum advantage for energy-constrained entanglement-assisted capacity. We exhibit that, in the energy-constrained situation, classical-quantum noisy channels can show improved capabilities under entanglement assistance, a phenomenon that is unattainable in the unrestricted scenario.

quant-ph↗

arXiv2025

Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability

We discover a new class of Gaussian bound entangled states of four-mode continuous-variable systems. These states appear as a transient phase when certain NPT-entangled Gaussian states are evolved under a noisy environment. A thermal bath comprising of harmonic oscillators is allowed to interact with one or modes of the system and a wide variety of initial Gaussian entangled (NPT as well as PPT) states are studied. The robustness of entanglement is defined as the time duration for which the entanglement of the initial state is preserved under the noisy dynamics. We access the separability by utilizing standard semi-definite programming techniques. While most states lose their entanglement after a certain time across all bi-partitions, an exception is observed for a three-parameter family of states which we call the generalized four-mode squeezed vacuum (gFMSV) states, which transitions to a bound entangled state, and remains so for a finite window of time. This dynamical onset of bound entanglement in continuous-variable systems is the central observation of our work. We carry out the analysis for Haar-random four-mode states (both pure and mixed) to scan the state space for transient bound entangled phase

quant-ph↗

arXiv2024

More nonlocality with less incompatibility in higher dimensions: Bell vs prepare-measure scenarios

Connecting incompatibility in measurements with the violation of local realism is one of the fundamental avenues of research. For two qubits, any incompatible pair of projective measurements can violate Clauser-Horne-Shimony-Holt (CHSH) inequality for some states, and there is a monotonic relationship between the level of measurement incompatibility (projective) and the violation. However, in the case of two qutrits, we exhibit that the violation of the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality responds non-monotonically with the amount of incompatibility; we term this more nonlocality with less incompatibility. Furthermore, unlike in the CHSH case, the maximally violating state in higher dimensions depends on the amount of measurement incompatibility. We illustrate that similar patterns can also be observed in an experimentally viable interferometric measuring technique. In such a measurement scenario, we provide an explicit example of incompatible (not jointly measurable) measurements that do not violate the CGLMP inequality for any shared quantum state. We extend our study of incompatibility in the prepare and measure scenario, focusing on quantum random access codes (QRACs). Surprisingly, we show that the monotonicity of average success probability with measurement incompatibility does not hold for higher dimensions, as opposed to two dimensions, even though the maximum probability of QRAC behaves monotonically with incompatibility.

quant-ph↗

arXiv2024

On the Convergence and Straightness of Rectified Flow

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing generation towards fewer sampling steps. However, the theoretical link between path geometry and sampling efficiency has been underexplored. This paper fills this gap by introducing a novel \textit{Piecewise Straightness} parameter, $\gamma_{2,T}$. We establish the first Wasserstein convergence bound that explicitly links the discretization error of \textit{any} general flow-model to $\gamma_{2,T}$, proving that minimizing curvature is the key to achieving high-fidelity, one-step sampling. Building on this theory, we establish the first theoretical framework to analyze the straightness of RF. We begin by offering intuitive geometric arguments for simple cases before identifying sufficient conditions under which a single rectification step (1-RF) yields a perfectly straight or even a Monge optimal coupling. While whether these sufficient conditions are met depends on the problem geometry, they enable the first concrete proofs in this area. Critically, fulfilling these conditions makes the subsequent flow (2-RF) perfectly straight ($\gamma_{2,T}=0$). This eliminates the discretization error in our bound and makes flawless, single-step sampling possible.

cs.LG↗

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

The communication power of a noisy qubit

A fundamental limitation of quantum communication is that a single qubit can carry at most 1 bit of classical information. For an important class of quantum communication channels, known as entanglement-breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the prize) hidden into one of four possible boxes, while avoiding a hazardous item (the bomb) hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum NOT channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.

quant-ph↗

arXiv2024

FLIPHAT: Joint Differential Privacy for High Dimensional Sparse Linear Bandits

High dimensional sparse linear bandits serve as an efficient model for sequential decision-making problems (e.g. personalized medicine), where high dimensional features (e.g. genomic data) on the users are available, but only a small subset of them are relevant. Motivated by data privacy concerns in these applications, we study the joint differentially private high dimensional sparse linear bandits, where both rewards and contexts are considered as private data. First, to quantify the cost of privacy, we derive a lower bound on the regret achievable in this setting. To further address the problem, we design a computationally efficient bandit algorithm, \textbf{F}orgetfu\textbf{L} \textbf{I}terative \textbf{P}rivate \textbf{HA}rd \textbf{T}hresholding (FLIPHAT). Along with doubling of episodes and episodic forgetting, FLIPHAT deploys a variant of Noisy Iterative Hard Thresholding (N-IHT) algorithm as a sparse linear regression oracle to ensure both privacy and regret-optimality. We show that FLIPHAT achieves optimal regret in terms of privacy parameters $\epsilon, \delta$, context dimension $d$, and time horizon $T$ up to a linear factor in model sparsity and logarithmic factor in $d$. We analyze the regret by providing a novel refined analysis of the estimation error of N-IHT, which is of parallel interest.

stat.ML↗

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↗