arXiv subjects

H. S. Karthik

Publications and source records attributed to H. S. Karthik.

At least 19 recordsLinked to original sources

arXiv2025

Quantum coherence leveraged agnostic phase estimation

Quantum metrology concerns improving the estimation of an unknown parameter using an optimal measurement scheme on the quantum system. More the optimality of the measurement, the better will be the improvement in sensing the value of the unknown parameter. Pertaining to the case of a two level system (qubit) undergoing rotation, a typical metrological task concerns the estimation of the angle of rotation ($τ$) given the information about the axis of rotation ($θ,ϕ$). The method for garnering information about ($τ)$ is through maximizing the Fisher information. In the absence of the axis-knowledge, the optimality of the metrological task reduces drastically. Drawing inspiration from recent works leveraging entanglement to connect closed time-like curves and metrology, we overcome this limitation (lack of the knowledge of the rotation axis) using an ancilla assisted protocol. Here, the probe and the ancilla interact through a coherently controlled superposition of unitary evolutions. The quantum coherence in the initial state of the ancilla forms as the resource aiding the protocol. By measuring the ancilla in the same coherent basis in which it was prepared, we achieve optimal Fisher information about the rotation angle, independent of the axis parameters. Notably, this resource-efficient and operationally simple agnostic sensing alternative is independent of both the entanglement in the initial joint state of the probe and the ancilla and entangling measurements, yet accounts for maximum Fisher information about the angle of rotation.

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arXiv2024

Noise-Resilient Quantum Random Access Codes

A $n^d \xrightarrow{p} 1$ Quantum Random Access Code (QRAC) is a communication task where Alice encodes $n$ classical bits into quantum states of dimension $d$ and transmits them to Bob, who performs appropriate measurements to recover the required bit with probability $p$. In the presence of a noisy environment, the performance of a QRAC is degraded, losing the advantage over classical strategies. We propose a practical technique that enables noise tolerance in such scenarios, recovering the quantum advantage in retrieving the required bit. We perform a photonic implementation of a $2^2 \xrightarrow {\text{p}} 1$ QRAC using polarization-encoded qubits under an amplitude-damping channel, where simple operations allow for noise robustness showing the revival of the quantum advantage when the noisy channel degrades the performance of the QRAC. This revival can be observed by violating a suitable dimension witness, which is closely related to the average success probability of the QRAC. This technique can be extended to other applications in the so-called prepare-and-measure scenario, enhancing the semi-device-independent protocol implementations.

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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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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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arXiv2017

N term pairwise correlation inequalities, steering and joint measurability

Chained correlation inequalities involving pairwise correlations of qubit observables in the equatorial plane are constructed based on the positivity of a sequence of moment matrices. When a jointly measurable set of fuzzy POVMs is employed in first measurement of every pair of sequential measurements, the chained pairwise correlations do not violate the classical bound imposed by the moment matrix positivity. We identify that incompatibility of measurements is only necessary, but not sufficient, in general, for the violation of the inequality. On the other hand, there exists a one-to-one equivalence between the degree of incompatibility (which quantifies the joint measurability) of the equatorial qubit observables and the optimal violation of a non-local steering inequality, proposed by Jones and Wiseman (Phys. Rev. A, 84, 012110 (2011)). To this end, we construct a local analogue of this steering inequality in a single qubit system and show that its violation is a mere reflection of measurement incompatibility of equatorial qubit POVMs, employed in first measurements in the sequential unsharp-sharp scheme.

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arXiv2015

Unsharp measurements and joint measurability

We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair of non-commuting observables in the presence of Bob's entangled quantum memory. We show that Bob should record the outcomes of incompatible (non-jointly measurable) POVMs in his quantum memory so as to beat the entropic uncertainty bound. In other words, in addition to the presence of entangled Alice-Bob state, implementing incompatible POVMs at Bob's end is necessary to beat the uncertainty bound and hence, predict the outcomes of non-commuting observables with improved precision. We also explore the implications of joint measurability to {\em validate} a moment matrix constructed from average pairwise correlations of three dichotomic non-commuting qubit observables. We prove that a classically acceptable moment matrix -- which ascertains the existence of a legitimate joint probability distribution for the outcomes of all the three dichotomic observables -- could be realized if and only if compatible POVMs are employed.

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arXiv2015

Joint Measurability and Temporal Steering

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed that a set of measurements is incompatible (i.e., not jointly measurable) if and only if it can be used for the demonstration of steering. In this paper, we prove the temporal analog of this result viz., a set of measurements are incompatible if and only if it exhibits temporal steering.

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arXiv2014

Joint measurability, steering and entropic uncertainty

The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or more measurements in the quantum scenario can be perceived from a classical point of view or they still exhibit non-classical features. Clearly, commuting observables can be measured jointly using projective measurements and their statistical outcomes can be discerned classically. However, such simple minded association of compatibility of measurements with commutativity turns out to be limited in an extended framework, where the usual notion of sharp projective valued measurements of self adjoint observables gets broadened to include unsharp measurements of generalized observables constituting positive operator valued measures (POVM). There is a surge of research activity recently towards gaining new physical insights on the emergence of classical behavior via joint measurability of unsharp observables. Here, we explore the entropic uncertainty relation for a pair of discrete observables (of Alice's system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable POVMs only. Within the joint measurability regime, the sum of entropies associated with Alice's measurement outcomes - conditioned by the results registered at Bob's end - are constrained to obey an entropic steering inequality. In this case, Bob's non-steerability reflects itself as his inability in predicting the outcomes of Alice's pair of non-commuting observables with better precision, even when they share an entangled state. As a further consequence, the quantum advantage envisaged for the construction of security proofs in key distribution is lost, when Bob's measurements are restricted to the joint measurability regime.

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arXiv2014

Quantum which-way information and fringe visibility when the detector is entangled with an ancilla

Quantum mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation is recently generalized by Banaszek et. al., (Nature Communications 4, 2594, 2013) when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability and the associated extended fringe visibility satisfying the duality inequality in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is non-zero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et. al., Nature Communications 4, 2594, 2013)) match identically with each other.

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arXiv2013

Entropic uncertainty assisted by temporal memory

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding entropies. Massen-Uffink entropic uncertainty relation (Phys. Rev. Lett. 60, 1103 (1988)) constrains the sum of entropies associated with incompatible measurements. The entropic uncertainty principle in the presence of quantum memory (Nature Phys. 6, 659 (2010)) brought about a fascinating twist by showing that quantum side information, enabled due to entanglement, helps in beating the uncertainty of non-commuting observables. Here we explore the interplay between temporal correlations and uncertainty. We show that with the assistance of a prior quantum temporal information achieved by sequential observations on the same quantum system at different times, the uncertainty bound on entropies gets reduced.

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arXiv2013

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.

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