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Prasanta K. Panigrahi

Publications and source records attributed to Prasanta K. Panigrahi.

At least 55 records · Page 3Linked to original sources
arXiv2024

A Geometry of entanglement and entropy

This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. Our focus centers on the connection between entanglement, von Neumann entropy, a measure of the information content within quantum systems and the geometry of composite Hilbert spaces. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective and elucidate how this connection unveils the nature of quantum entanglement, offering valuable insights into the underlying structure of quantum systems. This study underscores the significance of geometry as a key tool for understanding the rich landscape of quantum correlations and their implications across various domains of physics and information theory. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.

quant-ph↗
arXiv2024

Quantum Scissor from Exact Generalized Photon Number Statistics

We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The analytically obtained distributions are also capable of predicting the precise laser intensity windows for realizing a variety of quantum scissors. Truncating a photon added state overcomes the selection rule of obtaining the lower order Fock states. Photon addition also enables us to obtain a higher order Fock state in a lower order superposition. The importance of circular geometry is also demonstrated for engineering such quantum scissors.

quant-ph↗
arXiv2024

Information capacity analysis of fully correlated multi-level amplitude damping channels

The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multi-level amplitude damping channels. We investigate some of the information capacities of the simplest member of multi-level Amplitude Damping Channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.

quant-ph↗
arXiv2023

A Novel Approach to Threshold Quantum Images by using Unsharp Measurements

We propose a hybrid quantum approach to threshold and binarize a grayscale image through unsharp measurements (UM) relying on image histogram. Generally, the histograms are characterized by multiple overlapping normal distributions corresponding to objects, or image features with small but significant overlaps, making it challenging to establish suitable thresholds. The proposed methodology uses peaks of the overlapping Gaussians and the distance between neighboring local minima as the variance, based on which the UM parameters are chosen, that maps the normal distribution into a localized delta function. To demonstrate its efficacy, subsequent implementation is done on noisy quantum environments in Qiskit. This process is iteratively repeated for a multimodal histogram to obtain more thresholds, which are then applied to various life-like pictures to get high-contrast images, resulting in comparable peak signal-to-noise ratio and structural similarity index measure values. The obtained thresholds are used to binarize a grayscale image by using novel enhanced quantum image representation integrated with a threshold encoder and an efficient quantum comparator (QC) that depicts the whole binarized picture. This approach significantly reduces the complexity of the proposed QC and of the whole algorithm when compared to earlier models.

quant-ph↗
arXiv2023

Thermal effects in an imbalanced dipolar fermionic superfluid

We investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.

cond-mat.quant-gas↗
arXiv2023

Optimal non-Gaussian operations in difference-intensity detection and parity detection-based Mach-Zehnder interferometer

We investigate the benefits of probabilistic non-Gaussian operations in phase estimation using difference-intensity and parity detection-based Mach-Zehnder interferometers (MZI). We consider an experimentally implementable model to perform three different non-Gaussian operations, namely photon subtraction (PS), photon addition (PA), and photon catalysis (PC) on a single-mode squeezed vacuum (SSV) state. In difference-intensity detection-based MZI, two PC operation is found to be the most optimal, while for parity detection-based MZI, two PA operation emerges as the most optimal process. We have also provided the corresponding squeezing and transmissivity parameters at best performance, making our study relevant for experimentalists. Further, we have derived the general expression of moment-generating function, which shall be useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection.

quant-ph↗
arXiv2023

A Quantum Approach to solve N-Queens Problem

In this work, we have introduced two innovative quantum algorithms: the Direct Column Algorithm and the Quantum Backtracking Algorithm to solve N-Queens problem, which involves the arrangement of $N$ queens on an $N \times N$ chessboard such that they are not under attack from each other on the same row, column and diagonal. These algorithms utilizes Controlled W-states and dynamic circuits, to efficiently address this NP-Complete computational problem. The Direct Column Algorithm strategically reduces the search space, simplifying the solution process, even with exponential circuit complexity as the problem size grows, while Quantum Backtracking Algorithm emulates classical backtracking techniques within a quantum framework which allows the possibility of solving complex problems like satellite communication, routing and VLSI testing.

quant-ph↗
arXiv2023

'Complementarity' in paraxial and non-paraxial optical beams

Establishing the correspondence of two dimensional paraxial and three dimensional non-paraxial optical beams with the qubit and qutrit systems respectively, we derive a complementary relation between Hilbert-Schmidt coherence, generalized predictability and linear entropy. The linear entropy, a measure of mixedness is shown to saturate the complementarity relation for mixed bi-partite states. For pure two qubit and qutrit systems, it quantifies the global entanglement and reduces the complementarity relation to the triality relation between coherence, predictability and entanglement. We analyze these relations in wedge-product formalism in order to investigate the innate geometry of the complex vector space. The derived complementary relations offer insights into our ability to manipulate and utilize quantum properties for practical advancements.

quant-ph↗
arXiv2023

Geometrical Interpretation of Neutrino Oscillation with decay

The geometrical representation of two-flavor neutrino oscillation represents the neutrino's flavor eigenstate as a magnetic moment-like vector that evolves around a magnetic field-like vector that depicts the Hamiltonian of the system. In the present work, we demonstrate the geometrical interpretation of neutrino in a vacuum in the presence of decay, which transforms this circular trajectory of neutrino into a helical track that effectively makes the neutrino system mimic a classical damped driven oscillator. We show that in the absence of the phase factor $ξ$ in the decay Hamiltonian, the neutrino exactly behaves like the system of nuclear magnetic resonance(NMR); however, the inclusion of the phase part introduces a $CP$ violation, which makes the system deviate from NMR. Finally, we make a qualitative discussion on under-damped, critically-damped, and over-damped scenarios geometrically by three different diagrams. In the end, we make a comparative study of geometrical picturization in vacuum, matter, and decay, which extrapolates the understanding of the geometrical representation of neutrino oscillation in a more straightforward way.

hep-ph↗
arXiv2023

Stronger EPR-steering criterion based on inferred Schrodinger-Robertson uncertainty relation

Steering is one of the three in-equivalent forms of nonlocal correlations intermediate between Bell nonlocality and entanglement. Schrodinger-Robertson uncertainty relation (SRUR), has been widely used to detect entanglement and steering. However, the steering criterion in earlier works, based on SRUR, did not involve complete inferred-variance uncertainty relation. In this paper, by considering the local hidden state model and Reid formalism, we derive a complete inferred-variance EPR-steering criterion based on SRUR in the bipartite scenario. Furthermore, we check the effectiveness of our steering criterion with discrete variable bipartite two-qubit and two-qutrit isotropic states.

quant-ph↗
arXiv2023

Lorentzian path integral in Kantowski-Sachs anisotropic cosmology

Motivated by the recent development in quantum cosmology, we revisit the anisotropic Kantowski-Sachs model in the light of a Lorentzian path integral formalism. Studies so far have considered the Euclidean method where the choice of the lapse integration contour is constrained by certain physical considerations rather than mathematical justification. In this paper, we have studied the Hartle-Hawking no-boundary proposal along with the use of Picard-Lefschetz theory in performing the lapse integration. In an isotropic limit, we show our results agree with the studies made in FLRW cosmology. We also observe that in the large scale structure the no-boundary proposal tends towards a conical singularity at the beginning of time. We have also performed a massless scalar perturbation analysis with no back reaction. This reveals that if there were any perturbation present at the beginning of the universe then that would flare up at the final boundary.

gr-qc↗
arXiv2023

Tensile quantum-to-classical transition of macroscopic entangled states under complete coarse-grained measurements

The macroscopic limit at which the quantum-to-classical transition occurs remains as one of the long-standing questions in the foundations of quantum theory. There are evidences that the macroscopic limit to which the quantumness of a system persists depends on the degree of interaction due to the measurement processes. For instance, with a system having a considerably large Hilbert space dimension, if the measurement is performed in such a way that the outcome of the measurement only reveals a coarse-grained version of the information about the individual level of the concerned system then the disturbance due to the measurement process can be considered to be infinitesimally small. Based on such coarse-grained measurement the dependence of Bell inequality violation on the degree of coarsening has already been investigated [Phys. Rev. Lett. 112, 010402 (2014)]. In this paper, we first capture the fact that when local-realism is taken to be the defining notion of classicality, the effect of the degree of coarsening on the downfall of quantumness of a macroscopic entangled state can be compensated by testing a Bell-inequality of a higher number of settings from a family of symmetric Bell-inequalities if the number of settings is odd. However, on the contrary, we show that such compensation can not be seen when we witness such quantum-to-classical transition using symmetric Bell inequalities having an even number of settings. Finally, complementing the above result, we show that when unsteerability is taken as the classicality, for both odd and even numbers of settings the degree of coarsening at which the quantum-to-classical transition occurs can be consistently pushed ahead by testing a linear steering inequality of a higher number of settings and observing its violation. We further extend our treatment for mixed macroscopic entangled states

quant-ph↗
arXiv2023

CDF II W-mass anomaly and SO(10) GUT

The W-mass anomaly has yet to be established, but a huge proliferation of articles on the subject established the rich potential of such event. We investigate the SO(10) GUT constraints from the recently reported W-mass anomaly. We consider both Supersymmetric (SUSY) and non-supersymmetric (non-SUSY) grand unified theories by studying renormalization group equations (RGEs) for gauge coupling unification and their predictions on proton decay. In the non-SUSY models, single-stage unification is possible if one include a light (around TeV) real triplet Higgs scalar. However, these models predict speedy proton decay, inconsistent with the present experimental bound on the proton decay. This situation may be improved by including newer scalars and new intermediate-mass scales, which are present in the $SO(10)$ GUTs. The standard model is extended to a left-right symmetric model (LR), and the scale of LR breaking naturally introduces the intermediate scale in the model. A single-stage unification is possible even without including any triplet Higgs scalar in a minimal supersymmetric standard model.

hep-ph↗
arXiv2023

A symmetry perspective of the Riemann zeros

We study the relationship between the zeros of the Riemann zeta function and physical systems exhibiting supersymmetry, $PT$ symmetry and $SU(2)$ group symmetry. Our findings demonstrate that unbroken supersymmetry is associated with the presence of non-trivial zeros of the zeta function. However, in other cases, supersymmetry is spontaneously broken and the ground state energy of the system is not zero. Moreover, we have established the manifestation of PT symmetry invariance within our supersymmetric system. In addition, our findings provide insights into a $SU(2)$ symmetry that arises within these systems, with the Hilbert space having a two-level structure.

quant-ph↗
arXiv2023

Geometric genuine multipartite entanglement for four-qubit systems

Xie and Eberly introduced a genuine multipartite entanglement (GME) measure `concurrence fill'(\textit{Phys. Rev. Lett., \textbf{127}, 040403} (2021)) for three-party systems. It is defined as the area of a triangle whose side lengths represent squared concurrence in each bi-partition. However, it has been recently shown that concurrence fill is not monotonic under LOCC, hence not a faithful measure of entanglement. Though it is not a faithful entanglement measure, it encapsulates an elegant geometric interpretation of bipartite squared concurrences. There have been a few attempts to generalize GME measure to four-party settings and beyond. However, some of them are not faithful, and others simply lack an elegant geometric interpretation. The recent proposal from Xie et al. constructs a concurrence tetrahedron, whose volume gives the amount of GME for four-party systems; with generalization to more than four parties being the hypervolume of the simplex structure in that dimension. Here, we show by construction that to capture all aspects of multipartite entanglement, one does not need a more complex structure, and the four-party entanglement can be demonstrated using \textit{2D geometry only}. The subadditivity together with the Araki-Lieb inequality of linear entropy is used to construct a direct extension of the geometric GME to four-party systems resulting in quadrilateral geometry. Our measure can be geometrically interpreted as a combination of three quadrilaterals whose sides result from the concurrence in one-to-three bi-partition, and diagonal as concurrence in two-to-two bipartition.

quant-ph↗
arXiv2023

Exact Solutions of Augmented GP Equation: Solitons, Droplets and Supersolid

The augmented nonlinear Schrödinger equation (ANLSE), describing BEC, with the Lee-Huang-Yang (LHY) correction has exhibited a quantum droplet state, which has found experimental verification. In addition to the droplet, exact kink-antikink and supersolid phases have been recently obtained in different parameter domains. Interestingly, these solutions are associated with a constant background, unlike the form of BEC in quasi-one dimension, where dark, bright, and grey solitons have been experimentally obtained. Here, we connect a wide class of solutions of the ANLSE with the Jacobi elliptic functions using a fractional transformation method in a general scenario. The conserved energy and momentum are obtained in this general setting which differentiates and characterizes the different phases of the solution space. We then concentrate on the Jacobi-elliptic $dn(x, m^2)$ function, as the same is characterized by a non-vanishing background as compared to the other $cn$ and $sn$ functions.

nlin.PS↗
arXiv2023

Free Particle to Complex KdV breathers through Isospectral Deformation

The free particle in quantum mechanics in real space is endowed with supersymmetry, which enables a natural extension to complex spectra with a built-in parity (P) and time reversal (T) symmetry. It also explains the origin of unbroken and broken phases of the PT-symmetry and their relationship with the real and complex eigenvalues respectively, the latter further displaying zero-width resonances. This is possible as the extension of the eigenvalue problem to the complex plane enables the incorporation of bound and decaying states in the enlarged Hilbert space. The inherent freedom of modification of the potential without changing the spectra in supersymmetry naturally explains the connection of complex breather solutions of KdV with PT-symmetry and the free particle on the complex plane. Further, non-trivial zero-width resonances in the broken PT phase mandate a generalization that is directly connected to the sl(2, R) potential algebra.

math-ph↗
arXiv2023

Study of the Bound State, Electron-Detachment Energy and Reactivity of Hydride Ion using Variational Quantum Eigensolver

The accurate prediction and understanding of molecular energy and chemical reactivity are fundamental pursuits in the field of molecular quantum chemistry. With the limitations of the current noisy intermediate scale quantum computer (NISQ) era, the Variational Quantum Eigensolver (VQE) algorithm offers a promising approach to efficiently estimate the stable energy state of a given molecule. This study is focused on predicting the ground state and single electron detachment energy of the hydride ion because of its high electron electron correlation and numerous applications in astrophysics and quantum chemistry. The hydride ion is the first three body quantum problem for which the ground state energy has been calculated theoretically using the Chandrasekhar Wavefunction, which takes high electron-electron correlation into account. For the calculation of hydride ion, we used the VQE algorithm with two types of quantum computational ansatz, (i) chemistry inspired ansatz based on unitary CC (UCC) and (ii) hardware efficient based ansatz (HEA). To check the versatility of the algorithm, we analyzed two proton transfer reactions involving the hydride ion and finds the energy to be exothermic with a much improved result compared to previous studies. Overall, the VQE algorithm with a quantum computational approach is found to be reliable in calculating stable state energy, single electron detachment energy, and reaction energy for proton transfer reactions involving a highly correlated molecule with a low relative percentage error.

physics.chem-ph↗