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Anil Shaji

Publications and source records attributed to Anil Shaji.

At least 37 records · Page 2Linked to original sources
arXiv2021

Nonclassical correlations in subsystems of globally entangled quantum states

The relation between genuine multipartite entanglement in the pure state of a collection of N qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical correlations in the subsystem while the generalised geometric measure (GGM) [Phys. Rev. A. 81, 012308 (2010)] is used to quantify global entanglement in the N-qubit state. While no definite discernible dependence between the two can be found for randomly generated global states, for those with additional structure like weighted graph states we find that local discord is indicative of global multipartite entanglement. Global states that admit efficient classical descriptions like stabilizer states furnish an exception in which despite multipartite entanglement, nonclassical correlation is absent in two qubit subsystems. We discuss these results in the context of mixed state quantum computation where nonclassical correlation is considered a candidate resource that enables exponential speedup over classical computers.

quant-ph↗
arXiv2021

Nonclassical states of light in a nonlinear Michelson interferometer

Nonlinear quantum metrology schemes can lead to faster than Heisenberg limited scalings for the measurement uncertainty. We study a Michelson interferometer embedded in a Kerr medium [Luis and Rivas, Phys. Rev. A 92, 022104 (2015)] that leads to non-linear, intensity dependent phase shifts corresponding to relative changes in the lengths of its two arms. The quantum Cramer-Rao bound on the minimum achievable measurement uncertainties is worked out and the requirements, in practice, to saturate the bound are investigated. The choice of input state of light into the interferometer and the read out strategy at the output end are discussed. The ideal, non-classical states of light that must be used to saturate the bound are found to be highly susceptible to photon loss noise. We identify optimal states at each noise level that are both resilient to noise and capable of giving the enhanced sensitivities and discuss practical implementations of the interferometry scheme using such states.

quant-ph↗
arXiv2021

Open quantum dynamics with singularities: Master equations and degree of non-Markovianity

Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the generator of the corresponding master equation becomes singular. The first-order, time-local, homogeneous master equations then fail to describe the dynamics beyond the singular point. Retaining time-locality in the master equation necessitates a reformulation in terms of higher-order differential equations. We formulate a method to eliminate the divergent behavior of the generator by using a combination of higher-order derivatives of the generator with suitable weights and illustrate it with several examples. We also present a detailed study of the central spin model and we propose the average rate of information inflow in non-Markovian processes as a quantity that captures a different aspect of non-Markovian dynamics.

quant-ph↗
arXiv2021

Machine Learning the period finding algorithm

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.

quant-ph↗
arXiv2020

Photonic dephasing dynamics and role of initial correlations

Dynamics of open quantum systems depends on different types of initial correlations. On the one hand, when system and environment are both inherently multipartite, initial correlations between the parties of the composite environment make the dynamical map non-local, despite of local nature of the interaction between each party of the system and the environment. On the other hand, initial correlations between the open system and its environment prevents one from defining a completely positive dynamical map. Recently, dephasing dynamics of photons has been used in both of these frameworks - theoretically and experimentally - to demonstrate some fundamental and applicable aspects of open system dynamics and memory effects. However, the earlier studies in this context are often based solely on the concept of decoherence functions. Therefore, we still lack explicit master equation descriptions for dynamics induced by correlated composite initial environmental states. Also, a detailed understanding how initial system-environment correlations influence qubit dynamics in the photonic context is missing. In this paper, we derive generic master equations for the reduced dephasing dynamics of the two-photon polarization state when the bipartite environmental frequency degrees of freedom are initially correlated. We thereby show the explicit dependence of the operator form and the decay rates of the master equation on the initial frequency correlations and the influence of various types of frequency distributions. Furthermore, we use recently developed bath positive decomposition method to treat initially correlated polarization-frequency state of a photon, and demonstrate how this allows new insight and detailed information on how the contributions of different origin influence the photonic dephasing.

quant-ph↗
arXiv2019

Quantum steering in a qubit-field system

Quantum steering in a system consisting of a qubit coupled to a single-mode field is explored when classical-like measurements implemented by heterodyne detection schemes that collapse the state of the field on to a coherent state is considered. The quantum steering ellipsoid of the qubit is constructed to visualize the set of states on to which it can be steered using such measurements. In some cases, the steering set does not form an ellipsoid since only heterodyne detection is considered. Evolution of the steering ellipsoid corresponding to joint evolution of the qubit and field under the Jaynes-Cummins hamiltonian is also studied.

quant-ph↗
arXiv2019

Non-Markovian open dynamics from collision models

Convex combinations of the completely positive (CP) as well as CP-divisible, continuous time dynamical maps arising from collision models are investigated. While the individual maps are both CP and Markovian we find that convex combinations remain CP but not necessarily Markovian. Examples of such combinations for qubit dynamical maps arising from collisional models are worked out and the invertibility, CP-divisibility, P-divisibility as well as Markovian properties of such maps are explored.

quant-ph↗
arXiv2018

The reference system and not completely positive open quantum dynamics

Open quantum dynamics in a tripartite scenario including a system, its environment and a passive reference is shown to resolve several open questions regarding not completely positive (NCP) dynamical maps as valid descriptions of open quantum evolution. The steering states of the system and the environment with respect to the reference, reduced down to a dense, compact set of states of the system alone, provides a well defined domain of action for a bonafide dynamical map describing the open evolution of the system. The map is not restricted to being completely positive (CP) but it preserves the positivity of all states in its domain. NCP open dynamics corresponding to different initial configurations of the tripartite system are explored.

quant-ph↗
arXiv2017

Quantum Critical Environment Assisted Quantum Magnetometer

A central qubit coupled to an Ising ring of $N$ qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the Quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of $N$ values.

quant-ph↗
arXiv2017

Minimum Disturbance Rewards with Maximum Possible Classical Correlations

Weak measurements done on a subsystem of a bipartite system having both classical and nonClassical correlations between its components can potentially reveal information about the other subsystem with minimal disturbance to the overall state. We use weak quantum discord and the fidelity between the initial bipartite state and the state after measurement to construct a cost function that accounts for both the amount of information revealed about the other system as well as the disturbance to the overall state. We investigate the behaviour of the cost function for families of two qubit states and show that there is an optimal choice that can be made for the strength of the weak measurement.

quant-ph↗
arXiv2016

Two-mode Gaussian product states in a Lossy Interferometer

The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer-Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number for such input product states is compared to the limited scaling for dual squeezed vacuum states and for dual squeezed, displaced vacuum states.

quant-ph↗
arXiv2015

Weak measurements and nonClassical correlations

We extend the definition of quantum discord as a quantifier of nonClassical correlations in a quantum state to the case where weak measurements are performed on subsystem $A$ of a bipartite system $AB$. The properties of weak discord are explored for several families of quantum states. We find that in many cases weak quantum discord is identical to normal discord and in general the values of the two are very close to each other. Weak quantum discord reduces to discord in the appropriate limits as well. We also discuss the implications of these observations on the interpretations of quantum discord.

quant-ph↗
arXiv2015

The two-qubit amplitude damping channel: characterization using quantum stabilizer codes

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.

quant-ph↗
arXiv2015

The dynamics of a qubit reveals its coupling to a $N$ level system

Modeling the environment of a single qubit as an N dimensional quantum system, we show that the dynamics of the qubit alone, if measured in sufficient detail, can reveal the parameters of the qubit-environment coupling Hamiltonian. We show that data from quantum process tomography experiments can be used to get information about the environment that can be used to minimize its deleterious effects on the state of the qubit.

quant-ph↗
arXiv2015

The qubit reveals a qubit-cavity system

We show that the coupling between a qubit and a single mode cavity can be estimated from the process tomography data for the qubit alone. All the parameters of the coupling Hamiltonian between the qubit and the cavity mode can be obtained from observations on the qubit. We also show that the variance matrix and the photon number statistics of the single mode cavity can be reconstructed. Our results provide an alternate means of obtaining the coupling and reconstructing the state of the cavity mode in comparison with the techniques presently used.

quant-ph↗
arXiv2015

A simple model for exploring the role of quantum coherence and the environment in excitonic energy transfer

We investigate the role of quantum coherence in modulating the energy transfer rate between two independent energy donors and a single acceptor participating in an excitonic energy transfer process. The energy transfer rate depends explicitly on the nature of the initial coherent superposition state of the two donors and we connect it to the observed absorption profile of the acceptor and the stimulated emission profile of the energy donors. We consider simple models with mesoscopic environments interacting with the donors and the acceptor and compare the expression we obtained for the energy transfer rate with the results of numerical integration.

physics.chem-ph↗
arXiv2015

Entropic measures of nonclassical correlations

A framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of nonclassical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented.

quant-ph↗