arXiv subjects
Publications and source records attributed to R. Muthuganesan.
Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose a fidelity based valid measure of purity and coherence monotone and establish a relationship between them. This formulation of coherence is extended to quantum correlation relative to measurement. We have also studied the role of weak measurement on purity.
We examine thermal quantum correlations characterized by Measurement-Induced Nonlocality (MIN) in an infinite spin-1/2 Ising-Heisenberg spin chain with Dzyaloshinskii-Moriya (DM) interaction. We evaluate MIN analytically in the thermodynamic limit using the transfer matrix approach and show that the MIN and its first-order derivative may spotlight the quantum criticality and quantum phase transition (QPT). We observe that the DM interaction reduces the role of anisotropy parameter in initiating QPT. Further, the DM interaction also induces the nonlocality in the system if the spins are unentangled and greatly enhances the quantum correlations if the spins are correlated. The impact of the magnetic field and temperature on quantum correlations is also brought out at a critical point.
In quantum resource theory (QRT), asymmetry recognized as a valid resource for the advantage of various quantum information processing. In this paper, we establish the resource theory of asymmetry using quantum Fisher information (QFI). By defining the average Fisher information as a measure of asymmetry, it is shown that the discrepancy of bipartite global and local asymmetries naturally induces the nonclassical correlation between the subsystems. This measure satisfies all the necessary axioms of a faithful measure of bipartite quantum correlation. As an illustration, we have studied the proposed measure for an arbitrary pure state and Bell diagonal state.
In this article, we propose measurement-induced nonlocality (MIN) quantified by Hellinger distance using von Neumann projective measurement. The proposed MIN is a bonafide measure of nonlocal correlation and is resistant to local ancilla problem. We obtain an analytical expression of the Hellinger distance MIN for general pure and $2 \otimes n$ mixed states. In addition to comparing with similar measures, we explore the role of weak measurement in capturing nonlocal correlation.
Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair ofspin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local quantum Fisher information (lQFI). The effects of dipolar coupling constants on quantum correlation quantifiers are studied. The DM interaction greatly enhances the quantum correlation in the system whereas the temperature tends to annihilate the amount of quantum correlations.
By considering an exactly solvable model of a two interacting spin-1/2 qubits described by the Heisenberg anisotropic interaction in the presence of intrinsic decoherence, we study the dynamics of entanglement quantified by the concurrence and measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm and trace distance with different initial conditions. We highlight the relationship between the entanglement and MIN for the pure initial state. For an initial separable state, it is found that the robustness and the generation of the quantum correlations depend on the physical parameters. While considering the entangled state as an initial state, the results show that despite the phase decoherence all the correlations reach their steady state values after exhibiting some oscillations. Finally, we show that the existence of quantum correlation captured by MIN in the unentangled state.
In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement-induced nonlocality (MIN). Starting from an arbitrary Bell diagonal mixed states under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert-Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlation is observed. We show the existence of specific and important features of MIN such as revival, noise robustness and sudden change with respect to decoherence parameter. It is observed that all the noises cause sudden death of entanglement for partially entangled states. Further, we show the existence of separable quantum states with non-zero quantum correlations in terms of MIN.
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric to quantify closeness between two states. Using this metric, we introduce a valid quantum coherence measure. It is shown that the affinity based coherence measure is bounded by that based on fidelity and trace distance. Further, we propose a bipartite quantum correlation measure based on the affinity metric. The connection between the quantum correlation of states and its local coherence is established. The measure of quantumness in terms of difference of bipartite coherence and corresponding product state coherence is also identified. Finally, we interpret the operational meaning of the affinity based coherence as an upper bound of interferometric power of the quantum state.
Correlation beyond entanglement is a subject of interest in quantum information. Here we have shown the existence of quantum correlation without entanglement in Heisenberg $XYZ$ spin model with external magnetic field, using different versions of measurement-induced nonlocality. However maximally entangled states are shown to possess maximum correlation.
Geometric discord, a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. Original version of this measure is suffered by the local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all criteria of a good measure of quantum correlation of the bipartite system and resolves local ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically the proposed quantity for both pure and mixed states. For an arbitrary pure state, it is shown that affinity based geometric discord equal to geometric measure of entanglement. Further, we obtain a lower bound of this measure for m \times n dimensional arbitrary mixed state and a closed formula of proposed version of geometric discord for 2 \times n dimensional mixed state is obtained. Finally, as an illustration, we have studied the nonlocality of Bell diagonal state, isotropic and Werner states.
Measurement-induced nonlocality (MIN), a quantum correlation measure for the bipartite system, is an indicator of global effects due to locally invariant von Neumann projective measurements. It is well known fact that the correlation measures based on Hilbert-Schmidt norm are not credible measure in capturing nonlocal attributes of a quantum state. In this article, to remedy the local ancilla problem of Hilbert-Schmidt norm based MIN, we propose a new form of MIN-based on affinity. This quantity satisfies all criteria of a bonafide measure of quantum correlation measure. For an arbitrary pure state, it is shown that affinity based MIN equals to other forms of geometric versions of correlation measure. We obtain an upper bound of this measure for m \times n-dimensional arbitrary mixed state. We obtain a closed formula of the proposed version of MIN for 2 \times n dimensional (qubit qudit) mixed state. We apply these results on two-qubit mixed states such as Werner, isotropic and Bell diagonal state. To illustrate the robustness of affinity-based measure against noise, we study the dynamics of MIN under generalized amplitude damping channel.
Measurement Induced Nonlocality (MIN) captures nonlocal effects of a quantum state due to local von Neumann projective measurements, is a bonafide measure of quantum correlation between constituents of a composite system. In this paper, we study the dynamical behavior of entanglement (measured by concurrence), Hilber-Schmidt MIN and fidelity based MIN (FMIN) under local noisy channels such as hybrid (consists of bit, phase, bit and phase flip), generalized amplitude damping (GAD) and depolarizing channels for the initial Bell diagonal state. We observed that while sudden death of entanglement occur in hybrid and GAD channels, MIN and FMIN are more robust against such noise. Finally, we demonstrate the revival of MIN and FMIN after a dark point of time against depolarizing noise.
In this paper, we introduce quantum fidelity based measurement induced nonlocality for the bipartite state over two-sided von Neumann projective measurements. While all the properties of this quantity are reflected from that of one-sided measurement, the latter one is shown to set an upper bound for arbitrary bipartite state. As an illustration, we have studied the nonlocality of Bell diagonal state.
We study the dynamics of X-state for anisotropic Heisenberg spin system using quantum fidelity. It is shown that while Bell diagonal state, a special class of X-state, is stationary, there exists a set of two parametric states which are stationary in presence of external uniform magnetic field.
Measurement induced nonlocality (MIN) captures global nonlocal effect of bipartite quantum state due to locally invariant projective measurements. In this paper, we propose a new version of MIN using fidelity induced metric,andthe same is calculated for pure and mixed states. For mixed state, the upper bound is obtained from eigenvalues of correlation matrix. Further, dynamics of MIN and fidelity based MIN under various noisy quantum channels show that they are more robust than entanglement.
In this paper we propose measurement induced nonlocality (MIN) using a metric based on fidelity to capture global nonlocal effect of a quantum state due to locally invariant projective measurements. This quantity is a remedy for local ancilla problem in the original definition of MIN. We present an analytical expression of the proposed version of MIN for pure bipartite state and 2Xn dimensional mixed state. We also provide an upper bound of the MIN for general mixed state. Finally, we compare this quantity with MINs based on Hilbert-Schmidt norm and skew information for Werner and isotropic states.
In this paper we investigate the nonlocal correlation (beyond entanglement) captured by measurement induced nonlocality and geometric quantum discord for a pair of interacting spin-1/2 particles at thermal equilibrium. It is shown that both the measures are identical in measuring the correlation. We show the possibility of nonlocal correlation between the spins without entanglement, which ceases to exist only for the maximal mixture of product bases. We also observe that while interaction between the spins is responsible for the enhancement of correlation, this non-classicality decreases with the intervention of external magnetic field.