arXiv subjects

Gautam Sharma

Publications and source records attributed to Gautam Sharma.

At least 19 recordsLinked to original sources

arXiv2026

Hardware Realization of a Hamiltonian Simulation Algorithm for Time-Domain Maxwells Equations

We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic fields are discretized using finite-difference operators, and the resulting non-unitary matrices are mapped to Bell-basis Trotter blocks, enabling efficient circuit construction. We introduce a measurement procedure that retrieves not only field amplitudes, but also physical directions of the electric and magnetic field values at select spatial points. Implementing this logic on quantum hardware relies on relative-phase-based sign reconstruction. Numerical results obtained using IonQ QPU, show good agreement with analytical solutions of benchmark problems in two dimensions and on simulators; in three dimensions. We further extend our approach to compute fields scattered from simple bodies, by enforcing appropriate boundary conditions. Our work lays the foundational steps towards realizing quantum-hardware solutions for computational electromagnetics.

quant-ph↗

arXiv2025

Hamiltonian Simulation for Advection-Diffusion Equation with arbitrary transport field

We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving partial differential equations (PDEs), Hamiltonian simulation remains a relatively underexplored yet promising direction-particularly in the context of long-term, fault-tolerant quantum computing. Building on this potential, our quantum algorithm is designed to accommodate non-trivial, spatially varying transport fields and is applicable to both 2D and 3D advection-diffusion problems. To ensure numerical stability and accuracy, the algorithm combines an upwinding discretization scheme for the advective component and the central differencing for diffusion, adapted for quantum implementation through a tailored mix of approximation and optimization techniques. We demonstrate the algorithm's effectiveness on benchmark scenarios involving coupled rotational, shear, and diffusive transport in two and three dimensions. Additionally, we implement the 2D advection-diffusion equation using 16 qubits on IBM Quantum hardware, validating our method and highlighting its practical applicability and robustness.

quant-ph↗

arXiv2024

Certification of multi-qubit quantum systems with temporal inequalities

Demonstrating contextual correlations in quantum theory through the violation of a non-contextuality inequality necessarily needs some ``contexts" and thus assumes some compatibility relations between the measurements. As a result, any self-testing protocol based on the maximal violation of such inequality is not free from such assumptions. In this work, we propose temporal inequalities derived from non-contextuality inequalities for multi-qubit systems without assuming any compatibility relations among the measurements. We demonstrate that the new inequalities can be maximally violated via a sequential measurement scenario. Moreover, using the maximal violation of these temporal inequalities we are able to certify multi-qubit graph states and the measurements.

quant-ph↗

arXiv2024

Almost device-independent certification of GME states with minimal measurements

Device-independent certification of quantum states enables the characterization of states within a device under minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. Aiming to address this problem, we consider a multipartite quantum steering scenario involving an arbitrary number of parties, of which only one is trusted, meaning that the measurements performed by this party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each, which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states: graph states of arbitrary local dimension, Schmidt states of arbitrary local dimension, and $N$-qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states. Restricting to qubits, we also lift our almost device-independent scheme to device-independent self-testing.

quant-ph↗

arXiv2024

Bloch sphere analog of qudits using Heisenberg-Weyl Operators

We study an analogous Bloch sphere representation of higher-level quantum systems using the Heisenberg-Weyl operator basis. We introduce a parametrization method that will allow us to identify a real-valued Bloch vector for an arbitrary density operator. Before going into arbitrary $d$-level ($d\geq 3$) quantum systems (qudits), we start our analysis with three-level ones (qutrits). It is well known that we need at least eight real parameters in the Bloch vector to describe arbitrary three-level quantum systems (qutrits). However, using our method we can divide these parameters into four weight, and four angular parameters, and find that the weight parameters are inducing a unit sphere in four-dimension. And, the four angular parameters determine whether a Bloch vector is physical. Therefore, unlike its qubit counterpart, the qutrit Bloch sphere does not exhibit a solid structure. Importantly, this construction allows us to define different properties of qutrits in terms of Bloch vector components. We also examine the two and three-dimensional sections of the sphere, which reveal a non-convex yet closed structure for physical qutrit states. Further, we apply our representation to derive mutually unbiased bases (MUBs), characterize unital maps for qutrits, and assess ensembles using the Hilbert-Schmidt and Bures metrics. Moreover, we extend this construction to qudits, showcasing its potential applicability beyond the qutrit scenario.

quant-ph↗

arXiv2024

Monogamy and tradeoff relations for wave-particle duality information

The notions of predictability and visibility are essential in the mathematical formulation of wave particle duality. The work of Jakob and Bergou [Phys. Rev. A 76, 052107] generalises these notions for higher-dimensional quantum systems, which were initially defined for qubits, and subsequently proves a complementarity relation between predictability and visibility. By defining the single-party information content of a quantum system as the addition of predictability and visibility, and assuming that entanglement in a bipartite system in the form of concurrence mutually excludes the single-party information, the authors have proposed a complementarity relation between the concurrence and the single-party information content. We show that the information content of a quantum system defined by Jakob and Bergou is nothing but the Hilbert-Schmidt distance between the state of the quantum system of our consideration and the maximally mixed state. Motivated by the fact that the trace distance is a good measure of distance as compared to the Hilbert-Schmidt distance from the information theoretic point of view, we, in this work, define the information content of a quantum system as the trace distance between the quantum state and the maximally mixed state. We then employ the quantum Pinsker's inequality and the reverse Pinsker's inequality to derive a new complementarity and a reverse complementarity relation between the single-party information content and the entanglement present in a bipartite quantum system in a pure state. As a consequence of our findings, we show that for a bipartite system in a pure state, its entanglement and the predictabilities and visibilities associated with the subsystems cannot be arbitrarily small as well as arbitrarily large.

quant-ph↗

arXiv2023

Certification of two-qubit quantum systems with temporal inequality

Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Ref. [Phys. Rev. \textbf{A} 101, 032106 (2020)], a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this work, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from non-contextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.

quant-ph↗

arXiv2023

Negativity of Wigner distribution function as a measure of incompatibility

Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. Both of them are widely accepted resources in quantum information processing. We acquaint an approach to establish a connection between the negativity of the Wigner function, a well-known phase-space quasiprobability distribution, of finite-dimensional Hermitian operators and incompatibility among them. We calculate the negativity of the Wigner distribution function for noisy eigenprojectors of qubit Pauli operators as a function of the noise and observe that the amount of negativity increases with the decrease in noise vis-à-vis the increase in the incompatibility. It becomes maximum for the set of maximally unbiased operators. Our results, although qualitatively, provide a direct comparison between relative degrees of incompatibility among a set of operators for different amounts of noise. We generalize our treatment for higher dimensional qudits for specific finite-dimensional Gell-Mann operators to observe that with an increase in the dimension of the operators, the negativity of their Wigner distribution, and hence incompatibility, decreases.

quant-ph↗

arXiv2022

Impressive Electronic Transport in Be$_2$C Monolayer

We present thermoelectric properties of Be$_2$C monolayer based on density functional theory and semi-classical Boltzmann transport theory. Electronic structure calculations predict this material as a semiconductor with a direct bandgap of 2.0 eV computed using Gaussian-attenuating Perdew-Burke-Ernzerhof (Gau-PBE) hybrid functional. The Gau-PBE band structure is used to compute transport properties by solving the Boltzmann transport equation under the constant relaxation time approximation. In this work, we have explicitly determined the relaxation time by studying the electron-phonon interactions in the system to estimate absolute transport coefficients. Our results show that the monolayer possesses a high power factor ($\sim$ 3.44 mW/mK$^2$ @300K), similar to the commercial TE materials doped-Bi$_2$Te$_3$ and PbTe, suggesting that Be$_2$C monolayer is a promising thermoelectric material.

cond-mat.mtrl-sci↗

arXiv2021

Creation of quantum coherence with general measurement processes

Quantum measurement not only can destroy coherence but also can create it. Here, we estimate the maximum amount of coherence, one can create under a complete non-selective measurement process. For our analysis, we consider projective as well as POVM measurements. Based on our observations, we characterize the measurement processes into two categories, namely, the measurements with the ability to induce coherence and the ones without this ability. Our findings also suggest that the more POVM elements present in a measurement that acts on the quantum system, the less will be its coherence creating ability. We also introduce the notion of raw coherence in the POVMs that helps to create quantum coherence. Finally, we find a trade-off relation between the coherence creation, entanglement generation between system and apparatus, and the mixedness of the system in a general measurement setup.

quant-ph↗

arXiv2021

Information leak and incompatibility of physical context: A modified approach

A beautiful idea about the incompatibility of Physical Context(IPC) was introduced in Phys. Rev. A 102, 050201(R) (2020). Here, a context is defined as a set of a quantum state and two sharp rank-one measurements, and the incompatibility of physical context is defined as the leakage of information while implementing those two measurements successively in that quantum state. In this work, we show the limitations in their approach. The three primary limitations are that, (i) their approach is not positive operator-valued measurements and (ii), they restrict information-theoretic agents Alice, Eve and Bob to specific quantum operations and do not consider most general quantum operations i.e., quantum instruments and (iii), their measure of IPC can take negative values in specific cases in a more general scenario which implies the limitation of their information measure. Thereby, we have introduced a generalization and modification to their approach in more general and convenient way, such that this idea is well-defined for generic measurements, without these limitations. We also present a comparison of the measure of the IPC through their and our method. Lastly, we show, how the IPC reduces in the presence of memory using our modification, which further validates our approach.

quant-ph↗

arXiv2021

Role of fine-grained uncertainty in determining the limit of preparation contextuality

The optimal success probability of a communication game sets fundamental limitations on an operational theory. Quantum advantage of parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102, 010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of fine-grained uncertainty relation to the success probability of PORAC game played with the quantum resource. Subsequently, we find the optimal success probability for the 2-dit PORAC game using MUBs for the decoding strategy. Finally, we also derive an upper bound on quantum advantage for the N-dit PORAC game.

quant-ph↗

arXiv2021

Characterizing the generalized complementarity polytope with extractable information from MUBs

Complementarity polytope is a geometric structure that exists in N2-1 dimensional space for an N dimensional Hilbert space. The existence of N + 1 mutually unbiased bases(MUBs) is possible, if such a polytope can be shown to be a subset of density matrices, which is a very difficult task. With the hope of simplifying this task, we have shown in this work that, the complementarity polytope can be characterized by the total extractable information from N+1 MUBs. We also demonstrate that t less than (N+1) number of MUBs also form a polytope that exists in t(N-1) dimensional space, which we refer to as generalized complementarity polytope. The generalized complementarity polytope can also be characterized by total extractable information from t MUBs.

quant-ph↗

arXiv2021

A geometric way to find the measures of uncertainty from statistical divergences for discrete and finite probability distributions

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their properties. Further, we apply a similar technique to measure the uncertainty in the preparation of a quantum state.

quant-ph↗

arXiv2020

Robustness of interferometric complementarity under Decoherence

Interferometric complementarity is known to be one of the most nonclassical manifestations of the quantum formalism. It is commonly known as wave-particle duality and has been studied presently from the perspective of quantum information theory where wave and particle nature of a quantum system, called quanton, are characterised by coherence and path distinguishability respectively. We here consider the effect of noisy detectors on the complementarity relation. We report that by suitably choosing the initial quanton and the detector states along with the proper interactions between the quanton and the detectors, one can reduce the in uence of noisy environment on complementarity, thereby pushing it towards saturation. To demonstrate this, three kinds of noise on detectors and their roles on the saturation of the complementarity relation are extensively studied. We also observe that for fixed values of parameters involved in the process, asymmetric quanton state posses low value of coherence while it can have a higher amount of distinguishability, and hence it has the potential to enhance the duality relation.

quant-ph↗

arXiv2020

Improving the Optical and Thermoelectric Properties of Cs2InAgCl6 with Substitutional Doping: A DFT Insight

New generation Indium based lead-free Cs2InAgCl6 is a promising halide material in photovoltaic applications due to its good air stability and non-toxic behavior. But its wide band gap (>3 eV) is not suitable for solar spectrum and hence reducing the photoelectronic efficiency for device applications. Here we report a significant band gap reduction from 3.3 eV to 0.6 eV by substitutional doping and its effect on opto-electronic and opto-thermoelectric properties from first-principles study. The results predict that Sn/Pb and Ga & Cu co-doping enhance the density of states significantly near the valence band maximum (VBM) and thus reduce the band gap by shifting the VBM upward while the alkali-metals (K/Rb) slightly increase the band gap. A strong absorption peak near Shockley-Queisser limit is observed in co-doped case while in Sn/Pb-doped case, we notice a peak in the middle of the visible region of solar spectrum. The nature of band gap is indirect with Cu-Ga/Pb/Sn doping with a significant reduction in the band gap. We observe a significant increase in the power factor (PF) (2.03 mW/mK2) for n-type carrier in Pb-dpoing, which is ~3.5 times higher than the pristine case (0.6 mW/mK2) at 500 K.

cond-mat.mtrl-sci↗

arXiv2019

Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.

quant-ph↗

arXiv2018

Quantum uncertainty relation based on the mean deviation

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplicable. We apply the mean deviation based uncertainty relation to detect EPR violation in a lossy scenario for a higher inefficiency threshold than that allowed by the standard deviation based approach. We demonstrate that the mean deviation based uncertainty relation can perform equally well as the standard deviation based uncertainty relation as non-linear witness for entanglement detection.

quant-ph↗