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Namrata Shukla

Publications and source records attributed to Namrata Shukla.

14 recordsLinked to original sources
arXiv2026

Minimum uncertainty states and squeezed states from the sum uncertainty relation

Heisenberg uncertainty relation is at the origin of understanding minimum uncertainty states and squeezed states of light. In the recent past, sum uncertainty relation was formulated by Maccone and Pati [Maccone and Pati, Phys. Rev. Lett. 113, 260401 (2014)] which is claimed to be stronger than the existing Heisenberg-Robertson product uncertainty relation. We analyze the minimum uncertainty states for the sum uncertainty relation using the variational approach. We claim that the minimum uncertainty states for the sum uncertainty relation are always the minimum uncertainty states for the traditional product uncertainty relation, using the example of position-momentum pair as well as angular momentum operators. We show that the coherent and squeezed states of radiation remain completely unaffected by the sum uncertainty relation.

quant-ph↗
arXiv2023

Uncertainty Relation for Non-Hermitian Systems

We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of operators. We show that the cumulative gain in the quantum Fisher information when measuring two good observables for such non-Hermitian systems is way better than their Hermitian counterpart. Minimum uncertainty states being the best candidates for this gain near the exceptional point supports the intelligent or simultaneous non-Hermitian quantum sensors.

quant-ph↗
arXiv2021

Squeezed comb states

Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise.

quant-ph↗
arXiv2018

State-independent preparation uncertainty relations

The standard state-dependent Heisenberg-Robertson uncertainly-relation lower bound fails to capture the quintessential incompatibility of observables as the bound can be zero for some states. To remedy this problem, we establish a class of tight (i.e., inequalities are saturated)variance-based sum-uncertainty relations derived from the Lie algebraic properties of observables and show that our lower bounds depend only on the irreducible representation assumed carried by the Hilbert space of state of the system. We illustrate our result for the cases of the Weyl-Heisenberg algebra, special unitary algebras up to rank 4, and any semisimple compact algebra. We also prove the usefulness of our results by extending a known variance-based entanglement detection criterion.

quant-ph↗
arXiv2018

Quantum tetrachotomous states: Superposition of four coherent states on a line in phase space

The well studied quantum optical Schrödinger cat state is a superposition of two distinguishable states, with quantum coherence between these macroscopically distinguishable states being of foundational and, in the context of quantum-information processing, practical use. We refer to these quantum-optical cat states as quantum dichotomous states, reflecting that the state is a superposition of two options, and we introduce the term quantum multichotomous state to refer to a superposition of multiple macroscopically distinguishable options. For a single degree of freedom, such as position, we construct the quantum multichotomous states as a superposition of Gaussian states on the position line in phase space. Using this nomenclature, a quantum tetrachotomous state (QTS) is a coherent superposition of four macroscopically distinguishable states. We define, analyze and show how to create such states, and our focus on the QTS is due to their exhibition of much richer phenomena than for the quantum dichotomous states with lessons to going to general multichotomous states with the quantum comb state as a limiting case. Our characterization of the QTS involves the Wigner function, its marginal distributions, and the photon-number distribution, and we discuss the QTS's approximate realization in a multiple coupled-well system.

quant-ph↗
arXiv2017

Canonical Distillation of Entanglement

Distilling highly entangled quantum states from weaker ones is a process that is crucial for efficient and long-distance quantum communication, and has implications for several other quantum information protocols. We introduce the notion of distillation under limited resources, and specifically focus on the energy constraint. The corresponding protocol, which we call the canonical distillation of entanglement, naturally leads to the set of canonically distillable states. We show that for non-interacting Hamiltonians, almost no states are canonically distillable, while the situation can be drastically different for interacting ones. Several paradigmatic Hamiltonians are considered for bipartite as well as multipartite canonical distillability. The results have potential applications for practical quantum communication devices.

quant-ph↗
arXiv2016

Stronger Error Disturbance Relations for Incompatible Quantum Measurements

We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.

quant-ph↗
arXiv2016

Large Polarization Squeezing in Non-Degenerate Parametric Amplification of Coherent Radiation

Polarization squeezing is shown to occur in non-degenerate parametric amplification of coherent light and the degree of squeezing at interaction time $T$ can be as large as $1-e^{-2T}$. This gives $86.4\%$ polarization squeezing for $T=1$ and $98.2\%$ for $T=2$. One simple case when this occurs is on taking initially plane polarized light having equal amplitudes in the two modes that finally has equal intensities of two circular polarizations. This suggest the experimental settings of parameters to achieve this extent of polarization squeezing in coherent light.

quant-ph↗
arXiv2016

Polarization Squeezing in Degenerate Parametric Amplification of Coherent Light

We study polarization squeezing of a light beam initially in the coherent state using the nonlinear interaction hamiltonian $ H=k\big(\hat a_{x}^{\dagger2}+{\hat a_{x}}^2\big)$. For the degree of polarization squeezing, we use a definition written in the final form by the authors and also used in earlier papers. We find that the polarization squeezing can be very high and the degree of polarization squeezing can be less than unity by a very small amount. We achieve the polarization squeezing even for very low beam intensity under some conditions involving phase angles in the polarization modes.

quant-ph↗
arXiv2016

Pancharatnam phase deficit can detect macroscopic entanglement

The Pancharatnam phase deficit is defined as the difference between the Pancharat- nam phase acquired by the global system and the sum of the Pancharatnam phases acquired by subsystems during local unitary evolutions. We show that a non-zero value of the Pancharatnam phase deficit for a composite quantum system can be a signature of quantum entanglement. In the context of macroscopic quantum systems, we illustrate how the Pancharatnam phase deficit can be used to detect macroscopically entangled states. In particular, we use the Pancharatnam phase deficit to detect the entanglement for macroscopic superposition of coherent states. Furthermore, we show that by measuring the Pancharatnam phase deficit one can measure the concurrence of two spin singlets between distant boundaries.

quant-ph↗
arXiv2016

Construction of models of universe on the Riemann hypothesis

The aim of this note is to remove an implausible assumption in Moser's theorem \cite{JM} to establish our new theorem 1 which gives a lower estimate for the sum $p+c^2ρ$ on Riemann hypothesis. Corollary 1 gives a rather plausible construction of infinitely many models of universe with positive density($ρ$) and pressure($p$) since it makes use of the state equation in the form of an inequality.

math-ph↗
arXiv2016

Alteration in Non-Classicality of Light on Passing Through a Linear Polarization Beam Splitter

We observe the polarization squeezing in the mixture of a two mode squeezed vacuum and a simple coherent light through a linear polarization beam splitter. Squeezed vacuum not being squeezed in polarization, generates polarization squeezed light when superposed with coherent light. All the three Stokes parameters of the light produced on the output port of polarization beam splitter are found to be squeezed and squeezing factor also depends upon the parameters of coherent light.

physics.optics↗
arXiv2016

Simultaneous polarization squeezing in polarized N photon state and diminution on a squeezing operation

We study polarization squeezing of a pure photon number state which is obviously polarized but the mere change in the basis of polarization leads to simultaneous polarization squeezing in all the components of Stokes operator vector except those falling along or perpendicular to the direction of polarization state, is observed. We use the most general definition of polarization squeezing and discuss the experimental feasibility of the result. We also observe that a squeezing operation like non-degenerate parametric amplification of the state does not reveal simultaneous squeezing in all Stokes operator vectors and decreases in this sense.

quant-ph↗