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arXiv:2011.14703 · Annalen der Physik

Quantifying Quantum Correlation of Quasi‐Werner State and Probing Its Suitability for Quantum Teleportation

Arpita Chatterjee, Kishore Thapliyal, Anirban Pathak

Published Jul 5, 2021• 7 citations
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Abstract

Abstract The significance of photon addition in engineering the single‐ and two‐mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, the behavior of the Wigner function of two quasi‐Werner states constructed by superposing two normalized bipartite m‐photon added coherent states are analyzed. This allows the authors' to quantify the nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured using concurrence, entanglement of formation, and quantum discord. The WLN for a two‐mode state corresponds to the sum of the single‐mode nonclassicality and quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi‐Werner states as quantum channel for the teleportation of single‐mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. The non‐Gaussian operation is shown effective in stalling the detrimental effects of transmission through noisy channel and/or inefficient detection under realistic scenario. Further, in contrast to a set of existing results, it is established that the negative values of two‐mode Wigner function is not a witness of quantum correlation.

DOI
10.1002/andp.202100201

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Quantifying Quantum Correlation of Quasi‐Werner State and Probing Its Suitability for Quantum Teleportation (Ann. Phys. 10/2021)

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International Journal of Modern Physics B•Sep 13, 2016•5 citations
Abstract The significance of photon addition in engineering the single‐ and two‐mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, the behavior of the Wigner function of two quasi‐Werner states constructed by superposing two normalized bipartite m‐photon added coherent states are analyzed. This allows the authors' to quantify the nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured using concurrence, entanglement of formation, and quantum discord. The WLN for a two‐mode state corresponds to the sum of the single‐mode nonclassicality and quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi‐Werner states as quantum channel for the teleportation of single‐mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. The non‐Gaussian operation is shown effective in stalling the detrimental effects of transmission through noisy channel and/or inefficient detection under realistic scenario. Further, in contrast to a set of existing results, it is established that the negative values of two‐mode Wigner function is not a witness of quantum correlation.
Abstract The performance of adding or subtracting photons on two‐mode squeezed thermal states via examining the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two‐variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.
Glauber's coherent state is denoted by ∣α⟩\ketα∣α⟩ and its two-mode extension is represented by ∣α,β⟩\ket{α,β}∣α,β⟩. In this work, we introduce a two-mode superposition operator A=tab+ra†b†A=tab+ra^\dagger b^\daggerA=tab+ra†b†, whose action on the two-mode coherent state produces the two-mode coherent superposed quantum state ∣ψ⟩=(tab+ra†b†)∣α,β⟩\ketψ=(tab+ra^\dagger b^\dagger)\ket{α,β}∣ψ⟩=(tab+ra†b†)∣α,β⟩. We investigate the nonclassicality and quantum non-Gaussianity of this state by means of the Wigner distribution and Wigner logarithmic negativity. Once its intrinsic nonclassical and non-Gaussian structure is established, the state is employed as the entangled resource in the Braunstein-Kimble continuous-variable (CV) teleportation protocol. We compute the ideal teleportation fidelity for coherent and squeezed inputs and analyze how the strengths of nonclassicality and non-Gaussianity influence the teleportation efficiency. Our results identify specific parameter regimes where enhanced non-Gaussian features or increased nonclassicality enable fidelities beyond the classical threshold, thereby revealing the operational significance of engineered two-mode quantum states in CV quantum information processing.
Abstract We introduce a new state called photon-added-and-subtracted two modes pair coherent state (PAASTMPCS) by simultaneously adding and subtracting photons to the different modes of a pair coherent state. Its nonclassical and non-Gaussian properties are strengthened via the negative values of its Wigner function as the numbers of adding and subtracting photons are increased. It indicates that the PAASTMPCS is an entangled state. When increasing the numbers of photon-added and photon-subtracted to a pair coherent state, the degree of entanglement in the PAASTMPCS is enhanced compared with the original pair coherent state. By using a PAASTMPCS as a non-Gaussian entangled resource, the quantum teleportation processes are studied in detail. It is shown that the number sum and phase difference measurements protocol is more appropriate than the orthogonal quadrature components measurements protocol in the quantum teleportation process of a coherent state.
Abstract Quantum teleportation fundamentally depends on shared quantum correlations between spatially separated parties. Although entanglement is widely recognized as the primary resource enabling teleportation, quantum discord represents a more general form of nonclassical correlations that can persist even when entanglement is absent. We provide a thorough analysis combining analytical and numerical evaluations of quantum discord, negativity, and concurrence across varying noise parameters. The study includes simulations under both ide-alized and realistic noisy conditions, incorporating depolarizing noise models alongside experimentally relevant constraints. To improve quantum fidelity and accurately characterize quantum correlations in noisy environments, advanced error mitigation techniques—such as measurement error correction and zero-noise extrapolation—are applied. In this study, we focus on teleportation protocols utilizing two-qubit Werner states, which constitute a significant class of noisy mixed states modeling imperfect entanglement. We systematically examine how the teleportation fidelity varies as a function of the Werner mixing parameter λ and investigate its relationship with the corresponding quantum discord. Our findings indicate that quantum discord remains strictly greater than zero even in parameter regions where entanglement vanishes, emphasizing the role of discord in sustaining quantum advantages in teleportation schemes exposed to noise and imperfections. This highlights the importance of considering non-entanglement quantum correlations for a comprehensive understanding of teleportation resources in realistic settings.