arXiv subjects

Sahil

Publications and source records attributed to Sahil.

12 recordsLinked to original sources

arXiv2025

Unified Framework for Direct and Complete Characterization of an Unknown Kraus Operator and Density Matrix Using a Single Input State

Characterization of quantum measurements and dynamical processes is typically performed using pure state preparations. However, in realistic experimental settings, the preparation of pure states is often infeasible due to noise and system constraints. In this work, we present a unified framework that enables the direct and complete characterization of an unknown Kraus operator using only a single input state. The same framework also supports the characterization of unknown observable, unitary operator, and density matrix. Remarkably, all these tasks are accomplished using a single input state, a set of projector-based unitary evolution operators, and the measurement of a single observable. Importantly, our approach imposes no constraints on the strength of the coupling between the system and a probe.

quant-ph↗

arXiv2025

Unified Framework for Direct Characterization of Kraus Operators, Observables, Density Matrices, and Weak Values Without Weak Interaction

Generalized quantum measurements, described by positive operator-valued measures (POVMs), are essential for modeling realistic processes in open quantum systems. While quantum process tomography can fully characterize a POVM, it is resource-intensive and impractical when only specific POVM elements or matrix elements of a particular POVM element are of interest. Direct quantum measurement tomography offers a more efficient alternative but typically relies on weak interactions and complex structures of the system, environment, and probe as the dimension of the system increases, limiting its precision and scalability. Furthermore, characterizing a POVM element alone is insufficient to determine the underlying physical mechanism, as multiple Kraus operators can yield the same measurement statistics. In this work, we present a unified framework for the direct characterization of individual matrix elements of Kraus operators associated with specific POVM elements and arbitrary input states without requiring weak interaction, complex structures of the system-environment-probe or full process and state tomography. This framework naturally extends to projective measurements, enabling direct observable tomography, and to the characterization of unitary operations. Our method also captures modular and weak values of observables and Kraus operators, without invoking weak interaction approximations. We demonstrate potential implementations in optical systems, highlighting the experimental feasibility of our approach.

quant-ph↗

arXiv2025

Bochner's theorem for finite inverse semigroups and its connection to Choi's theorem

Bochner's theorem characterizes positive definite functions on groups through the positivity of their Fourier transforms and plays a fundamental role in Harmonic analysis. While Bochner-type results are known for certain classes of semigroups, they typically differ from the group theoretic formulations and do not retain the same level of simplicity and generality. In this work, we prove a Bochner-type theorem for finite inverse semigroups at the level of matrix valued linear maps on the contracted algebras of the semigroups. Using the intrinsic partial order of inverse semigroups, positivity naturally arises through a M\"obius-transformed map. Our main result characterizes the positive definiteness of the M\"obius transformed map in terms of the positivity of the Fourier transform of the original map with respect to a complete family of inequivalent irreducible representations of the contracted algebra induced by irreducible unitary representations of the maximal subgroups of the inverse semigroup. The proof relies on Fourier inversion formula, Schur orthogonality relations, and alternative characterizations of positive definite maps, all established here in the setting of finite inverse semigroups. As a special case, we show that for the inverse semigroup of matrix units, Bochner's theorem reduces exactly to Choi's characterization of completely positive maps.

math-ph↗

arXiv2025

Architecting Digital Twins for Intelligent Transportation Systems

Modern transportation systems face growing challenges in managing traffic flow, ensuring safety, and maintaining operational efficiency amid dynamic traffic patterns. Addressing these challenges requires intelligent solutions capable of real-time monitoring, predictive analytics, and adaptive control. This paper proposes an architecture for DigIT, a Digital Twin (DT) platform for Intelligent Transportation Systems (ITS), designed to overcome the limitations of existing frameworks by offering a modular and scalable solution for traffic management. Built on a Domain Concept Model (DCM), the architecture systematically models key ITS components enabling seamless integration of predictive modeling and simulations. The architecture leverages machine learning models to forecast traffic patterns based on historical and real-time data. To adapt to evolving traffic patterns, the architecture incorporates adaptive Machine Learning Operations (MLOps), automating the deployment and lifecycle management of predictive models. Evaluation results highlight the effectiveness of the architecture in delivering accurate predictions and computational efficiency.

cs.LG↗

arXiv2024

Post-Markovian master equation \`{a} la microscopic collisional model

We derive a completely positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological master equation is both analytically solvable and numerically tractable. Depending on the choice of the memory kernel function, the PMME can be reduced to the exact Nakajima-Zwanzig equation or the Markovian master equation, enabling a broad spectrum of dynamical behaviors. We also investigate thermalization using the derived equation, revealing that the post-Markovian dynamics accelerates the thermalization process, exceeding rates observed within the Markovian framework. Our approach solidifies the assertion that "collisional models can simulate any open quantum dynamics", underscoring the versatility of the models in realizing open quantum systems.

quant-ph↗

arXiv2024

Nirjas: An open source framework for extracting metadata from the source code

Metadata and comments are critical elements of any software development process. In this paper, we explain how metadata and comments in source code can play an essential role in comprehending software. We introduce a Python-based open-source framework, Nirjas, which helps in extracting this metadata in a structured manner. Various syntaxes, types, and widely accepted conventions exist for adding comments in source files of different programming languages. Edge cases can create noise in extraction, for which we use Regex to accurately retrieve metadata. Non-Regex methods can give results but often miss accuracy and noise separation. Nirjas also separates different types of comments, source code, and provides details about those comments, such as line number, file name, language used, total SLOC, etc. Nirjas is a standalone Python framework/library and can be easily installed via source or pip (the Python package installer). Nirjas was initially created as part of a Google Summer of Code project and is currently developed and maintained under the FOSSology organization.

cs.SE↗

arXiv2024

State-dependent and state-independent uncertainty relations for skew information and standard deviation

In this work, we derive state-dependent uncertainty relations (uncertainty equalities) in which commutators of incompatible operators (not necessarily Hermitian) are explicitly present and state-independent uncertainty relations based on the Wigner-Yanase (-Dyson) skew information. We derive uncertainty equality based on standard deviation for incompatible operators with mixed states, a generalization of previous works in which only pure states were considered. We show that for pure states, the Wigner-Yanase skew information based state-independent uncertainty relations become standard deviation based state-independent uncertainty relations which turn out to be tighter uncertainty relations for some cases than the ones given in previous works, and we generalize the previous works for arbitrary operators. As the Wigner-Yanase skew information of a quantum channel can be considered as a measure of quantum coherence of a density operator with respect to that channel, we show that there exists a state-independent uncertainty relation for the coherence measures of the density operator with respect to a collection of different channels. We show that state-dependent and state-independent uncertainty relations based on a more general version of skew information called generalized skew information which includes the Wigner-Yanase (-Dyson) skew information and the Fisher information as special cases hold. In qubits, we derive tighter state-independent uncertainty inequalities for different form of generalized skew informations and standard deviations, and state-independent uncertainty equalities involving generalized skew informations and standard deviations. Finally, we provide a scheme to determine the Wigner-Yanase (-Dyson) skew information of an unknown observable using the notion of weak values.

quant-ph↗

arXiv2023

Duality between quantum channels and super-channels is basis-dependent

The complete positivity vs positivity correspondence in the Choi-Jamio{\l}kowski-Kraus-Sudarshan quantum channel-state isomorphism depends on the choice of basis. Instead of the "canonical" basis, if we use, e.g., the Pauli spin matrices along with the identity as the basis for the space of bounded operators on the two-dimensional complex Hilbert space, this correspondence breaks down. A sufficient condition on the basis for validity of this correspondence is provided in the work of Paulsen and Shult~\cite{Paulsen}, which was later proven to be necessary by Kye~\cite{Kye}. A correspondence is also present between the space of super-maps and the tensor product of the spaces of the inputs and outputs of the same. In particular, a super-map is completely CP-preserving if and only if its Choi-type representation is completely positive (CP). This correspondence also depends on a specific choice of basis. In this work, we find the necessary and sufficient condition on a basis such that this correspondence holds true.

quant-ph↗

arXiv2023

Exact Quantum Speed Limits

The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for the unitary dynamics of pure-state quantum system that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control and quantum thermal machines.

quant-ph↗

arXiv2022

Uncertainty Relations in Pre- and Post-Selected Systems

In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have physical meanings which we present here. We demonstrate two unusual properties in the PPS system using our uncertainty relation. First, for commuting observables, the lower bound of the uncertainty relation in the PPS system does not become zero even if the initially prepared state i.e., pre-selection is the eigenstate of both the observables when specific post-selections are considered. This implies that for such case, two commuting observables can disturb each other's measurement results which is in fully contrast with the Robertson-Heisenberg uncertainty relation. Secondly, unlike the standard quantum system, the PPS system makes it feasible to prepare sharply a quantum state (pre-selection) for non-commuting observables {(to be detailed in the main text)}. Some applications of uncertainty and uncertainty relation in the PPS system are provided: $(i)$ detection of mixedness of an unknown state, $(ii)$ stronger uncertainty relation in the standard quantum system, ($iii$) ``purely quantum uncertainty relation" that is, the uncertainty relation which is not affected (i.e., neither increasing nor decreasing) under the classical mixing of quantum states, $(iv)$ state dependent tighter uncertainty relation in the standard quantum system, and $(v)$ tighter upper bound for the out-of-time-order correlation function.

quant-ph↗

arXiv2021

Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection

Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally important in the sense that they are useful to resolve some paradoxes, realize strange quantum effects, reconstruct density matrices, etc. In this work, we show that it is possible to access the higher moment weak values of an observable using weak values of that observable with pairwise orthogonal post-selections. Although the higher moment weak values of an observable are inaccessible with Gaussian pointer states, our method allows any pointer state. We have calculated product weak values in a bipartite system for any given pure and mixed pre selected states. Such product weak values can be obtained using only the measurements of local weak values (which are defined as single system weak values in a multi-partite system). As an application, we use higher moment weak values and product weak values to reconstruct unknown quantum states of single and bipartite systems, respectively. Further, we give a necessary separability criteria for finite dimensional systems using product weak values and certain class of entangled states violate this inequality by cleverly choosing the product observables and the post selections. By such choices, positive partial transpose (PPT) criteria can be achieved for these classes of entangled states. Robustness of our method which occurs due to inappropriate choices of quantum observables and noisy post-selections is also discussed here. Our method can easily be generalized to the multi-partite systems.

quant-ph↗

arXiv2015

Dynamic Cluster Head Selection Using Fuzzy Logic on Cloud in Wireless Sensor Networks

One of the most vital activities to reduce energy consumption in wireless sensor networks is clustering. In clustering, one node from a group of nodes is selected to be a cluster head, which handles majority of the computation and processing for the nodes in the cluster. This paper proposes an algorithm for fuzzy based dynamic cluster head selection on cloud in wireless sensor networks. The proposed algorithm calculates a Potential value for each node and selects cluster heads with high potential. The proposed algorithm minimizes cluster overlapping by spatial distribution of cluster heads and discards malicious nodes i.e. never allows malicious nodes to be cluster heads.

cs.NI↗