arXiv subjects

A. R. Usha Devi

Publications and source records attributed to A. R. Usha Devi.

At least 19 recordsLinked to original sources

arXiv2026

Dicke superposition probes for noise-resilient Heisenberg and super-Heisenberg Metrology

Phase sensing with entangled multi-qubit states in the presence of noise is a central theme of modern quantum metrology. The present work investigates Dicke state superposition probes for quantum phase sensing under parameter encoding generated by one- and two-body interaction Hamiltonians. Under linear collective-spin encoding, near-optimal Dicke superposition states are shown to exhibit significantly enhanced robustness against phase damping noise compared with Greenberger--Horne--Zeilinger (GHZ), W-superposition, and balanced Dicke states, while maintaining favorable metrological performance under realistic decoherence channels. For two-body interactions, optimal probe states maximizing the quantum Fisher information are identified. Their noise resilience and metrological scaling behaviour under phase damping, amplitude damping, and global depolarizing channels are analyzed. The associated near-optimal Dicke superposition states are found to exhibit improved resilience to phase damping, for the system sizes considered. These results establish tailored near-optimal Dicke state superposition probes as versatile and noise-resilient resources for Heisenberg and super-Heisenberg quantum phase sensing governed by one- and two-body interactions.

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arXiv2025

Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka

We present a three-qubit quantum state tomography scheme requiring a set of 17 measurement settings, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurement settings. Using IBM's 127-qubit open-access quantum processor ibm osaka, we prepare the three-qubit W state and employ our tomography scheme to reconstruct it. Additionally, we implement a two-qubit tomography protocol, involving 7 measurement settings, on ibm osaka to reconstruct two of the two-qubit marginals of the W state. This serves as a {\em proof-of-principle} demonstration of the well-known theoretical result that any two of the two-qubit reduced density matrices can uniquely determine most of the whole three-qubit pure states. We show that the fidelity of the W-state reconstructed from its two-qubit subsystems is consistently larger than that obtained from the full three-qubit tomography, highlighting the practical advantage of the subsystem-based tomography approach.

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arXiv2024

Enhanced non-macrorealism: Extreme violations of Leggett-Garg inequalities for a system evolving under superposition of unitaries

Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. We show that a system, upon subjecting to transform under superposition of unitary operators, exhibits enhanced non-macrorealistic feature - as quantified by violation of the Leggett-Garg inequality (LGI) beyond the temporal Tsirelson bound. Moreover, this superposition of unitaries also provides robustness against decoherence by allowing the system to violate LGI and thereby retain its non-macrorealistic behavior for a strikingly longer duration. Using an NMR register, we experimentally demonstrate the superposition of unitaries with the help of an ancillary qubit and verify these theoretical predictions.

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arXiv2024

Lorentz canoncial forms of two-qubit states

The Bloch sphere provides an elegant way of visualizing a qubit. Analogous representation of the simplest composite state of two-qubits has attracted significant attention. Here we present a detailed mathematical analysis of the real-matrix parametrization and associated geometric picturization of arbitrary two-qubit states - up to their local SL2C equivalence, in terms of canonical ellipsoids inscribed within the Bloch sphere.

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arXiv2022

Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

We show that the pure entangled three-qubit symmetric states which are inequivalent under stochastic local operations and classcial communication (SLOCC) exhibit distinct geometric representation in terms of a spheroid inscribed within the Bloch sphere. We provide detailed analysis of the SLOCC canonical forms of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states. Based on the Lorentz canonical forms of these states we arrive at two different geometrical representations: (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure permutation symmetric three-qubit states constructed from 3 distinct spinors and (ii) a spheroid centered at (0,0,1/2) inside the Bloch sphere, with fixed semiaxes lengths (1/sqrt{2}, 1/sqrt{2}, 1/2) when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors.

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arXiv2022

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

We show that violation of variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi~[Phys.Rev.A {\bf 68}, 032103 (2003)], reflects entanglement in the equal bipartitions of an $N$-qubit symmetric state with even qubits. We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix [Phys. Lett. A, {\bf 364}, 203 (2007)] of the two-qubit reduced system of a permutation symmetric $N$-qubit state.

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arXiv2022

Margenau-Hill operator valued measures and joint measurability

We employ the Margenau-Hill (MH) correspondence rule for associating classical functions with quantum operators to construct quasi-probability mass functions. Using this we obtain the fuzzy one parameter quasi measurement operator (QMO) characterizing the incompatibility of non-commuting spin observables of qubits, qutrits and 2-qubit systems. Positivity of the fuzzy MH-QMO places upper bounds on the associated unsharpness parameter. This serves as a sufficient condition for measurement incompatibility of spin observables. We assess the amount of unsharpness required for joint measurability (compatibility) of the non-commuting qubit, qutrit and 2-qubit observables. We show that the {\em degree of compatibility} of a pair of orthogonal qubit observables agrees perfectly with the necessary and sufficient conditions for joint measurability. Furthermore, we obtain analytical upper bounds on the unsharpness parameter specifying the range of joint measurability of spin components of qutrits and pairs of orthogonal spin observables of a 2-qubit system. Our results indicate that the measurement incompatibility of spin observables increases with Hilbert space dimension.

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arXiv2022

Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

The quantum steering ellipsoid inscribed inside the Bloch sphere offers an elegant geometric visualization of two-qubit states shared between Alice and Bob. The set of Bloch vectors of Bob's qubit, steered by Alice via all possible local measurements on her qubit, constitutes the steering ellipsoid. The steering ellipsoids are shown to be effective in capturing quantum correlation properties, such as monogamy, exhibited by entangled multiqubit systems. We focus here on the canonical ellipsoids of two-qubit states realized by incorporating optimal local filtering operations by Alice and Bob on their respective qubits. Based on these canonical forms we show that the reduced two-qubit states drawn from pure entangled three-qubit permutation symmetric states, which are inequivalent under stochastic local operations and classcial communication (SLOCC), carry distinct geometric signatures. We provide detailed analysis of the SLOCC canonical forms and the associated steering ellipsoids of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states: We arrive at (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure symmetric three-qubit states constructed by permutation of 3 distinct spinors and (ii) an oblate spheroid centered at $(0,0,1/2)$ inside the Bloch sphere, with fixed semiaxes lengths (1/Sqrt[2],\, 1/Sqrt[2],\, 1/2)), when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors. We also explore volume monogamy relations formulated in terms of the volumes of the steering ellipsoids of the SLOCC inequivalent pure entangled three-qubit symmetric states.

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arXiv2021

Characterizing nonlocality of pure symmetric three-qubit states

We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys. Rev. A, 96, 062310 (2017)) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state do not violate the CHSH inequality and hence they are CHSH-local. However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting of two and three distinct spinors (qubits) respectively, can be distinguished based on the strength of violation in the conditional CHSH nonlocality test. Furthermore, we identify six of the 46 classes of tight Bell inequalities in the three-party, two-setting, two-outcome i.e., (3,2,2) scenario (Phys. Rev. A 94, 062121 (2016)). Among the two inequivalent families of three-qubit pure symmetric states, only the states belonging to three distinct spinor class show maximum violations of these six tight Bell inequalities.

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arXiv2021

Canonical structures of $A$ and $B$ forms

In their seminal paper (Phys. Rev.121, 920 (1961)) Sudarshan, Mathews and Rau investigated properties of the dynamical $A$ and $B$ maps acting on $n$ dimensional quantum systems. Nature of the dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the $A$ and $B$ dynamical maps has not received its due attention. In this tutorial article we review the properties of $A$ and $B$ forms associated with the dynamics of finite dimensional quantum systems. In particular we investigate a canonical structure associated with the $A$ form and establish its equivalence with the associated $B$ form. We show that the canonical structure of the $A$ form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.

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arXiv2021

Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits

We investigate the notion of uncertainty region using the variance based sum uncertainty relation for qubits and qutrits.We compare uncertainty region of the qubit (a 2-level system) with that of the qutrit (3-level system) by considering sum uncertainty relation for two non-commuting Pauli-like observables, acting on the two dimensional qubit Hilbert space. We identify that physically valid uncertainty region of a qubit is smaller than that of a qutrit. This implies that an enhanced precision can be achieved in the measurement of incompatible Pauli-like observables acting on the 2-dimensional subspace of a qutrit Hilbert space. We discuss the implication of the reduced uncertainties in the steady states of Lambda, V and Cascade types of 3-level atomic systems. Furthermore, we construct a two-qubit permutation symmetric state, corresponding to a 3-level system and show that the reduction in the sum uncertainty value -- or equivalently, increased uncertainty region of a qutrit system { is a consequence of quantum entanglement in the two-qubit system. Our results suggest that uncertainty region can be used as a dimensional witness.

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arXiv2020

Canonical forms of two-qubit states under local operations

Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding non-locality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown (Verstraete et.al. {Phys. Rev. A, 64, 010101(R) (2001)) that an arbitrary two-qubit state gets transformed under SLOCC into one of the {\em two} different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other non-diagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et.al. required highly non-trivial results on matrix decompositions in $n$ dimensional spaces with indefinite metric. Here we employ an entirely different approach -- inspired by the methods developed by Rao et. al., (J. Mod. Opt. 45, 955 (1998)) in classical polarization optics -- which leads naturally towards the identification of two inequivalent SLOCC invariant canonical forms for two-qubit states. In addition, our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.

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arXiv2019

Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics

We investigate the three-term Leggett-Garg inequality (LGI) for a two-level quantum system undergoing parity-time (PT ) symmetric dynamics governed by a non-Hermitian Hamiltonian, when a sequence of dichotomic projective measurements are carried out at different time intervals. In contrast to the case of coherent unitary dynamics, violation of LGI is shown to increase beyond the temporal Tsirelson bound approaching the algebraic maximum in the limit of the spontaneous PT symmetry breaking

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arXiv2018

Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors

Majorana geometric representation of pure N-qubit states obeying exchange symmetry is em- ployed to explore spin squeezing properties in the family of states with two distinct spinors. Dicke states are characterized by two orthogonal spinors and belong to this family - but they are not spin squeezed. On the otherhand, those constituted by two non-orthogonal spinors exhibit spin squeezing.

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arXiv2018

Quantum hypothesis testing and state discrimination

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.

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arXiv2017

One Parameter family of N-qudit Werner-Popescu states: Bipartite separability using conditional quantum relative Tsallis entropy

The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner- Popescu states in their 1 : N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit q tending to infinity and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe- Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.

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arXiv2017

Asymptotic spectral stability of the Gisin-Percival state diffusion

Starting from the Gisin-Percival state diffusion equation for the pure state trajectory of a composite bipartite quantum system and exploiting the purification of a mixed state via its Schmidt decomposition, we write the diffusion equation for the quantum trajectory of the mixed state of a subsystem $S$ of the bipartite system, when the initial state in $S$ is mixed. Denoting the diffused state of the system $S$ at time $t$ by $ρ_t(\mathbf{B})$ for each $t\geq 0$, where $\mathbf{B}$ is the underlying complex $n$-dimensional vector-valued Brownian motion process and using It{ô} calculus, along with an induction procedure, we arrive at the stochastic differential of the scalar-valued moment process ${\rm Tr}[ρ_t^m( \mathbf{B})], \,\,\, m=2,3,\ldots$ in terms of $d\,\mathbf{B}$ and $d\,t$. This shows that each of the processes $\{{\rm Tr}[ρ_t^m( \mathbf{B})], t\geq 0\}$ admits a Doob-Meyer decomposition as the sum of a martingale $M^{(m)}_t(\mathbf{B})$ and a non-negative increasing process $S^{(m)}_t(\mathbf{B})$. This ensures the existence of $\underset{t\rightarrow\infty}{\lim}\, {\rm Tr}[ρ_t^m( \mathbf{B})]$ almost surely with respect to the Wiener probability measure $μ$ of the Brownian motion $\mathbf{B}$, for each $m=2,\, 3,\, \ldots$. In particular, when $S$ is a finite level system, the spectrum and therefore the entropy of $ρ_t (\mathbf{B})$ converge almost surely to a limit as $t\rightarrow \infty$. In the Appendix, by employing probabilistic means, we prove a technical result which implies the almost sure convergence of the spectrum for countably infinite level systems.

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arXiv2017

From quantum stochastic differential equations to Gisin-Percival state diffusion

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy (Comm. Math. Phys. 93, 301 (1984)) and exploiting the Wiener-Ito-Segal isomorphism between the Boson Fock reservoir space $Γ(L^2(\mathbb{R}_+)\otimes (\mathbb{C}^{n}\oplus \mathbb{C}^{n}))$ and the Hilbert space $L^2(μ)$, where $μ$ is the Wiener probability measure of a complex $n$-dimensional vector-valued standard Brownian motion $\{\mathbf{B}(t), t\geq 0\}$, we derive a non-linear stochastic Schrodinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion $\mathbf{B}$. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation (J. Phys. A, 167, 315 (1992)). This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a radomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

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