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Physical Review A

Analysis of necessary and sufficient conditions for quantum teleportation with non-Gaussian resources

Soumyakanti Bose, Manoranjan Kumar

Published Mar 26, 2021• 7 citations
Publisher

Abstract

Recent theoretical and experimental advances have demonstrated advantages of using non-Gaussian optical resources compared to the Gaussian ones in the context of quantum teleportation (QT), an important quantum information processing task. From both theoretical and experimental points of view the question of which attributes of the resources, besides entanglement, render them useful for QT is an important one. In this paper, we examine the question of whether two well-studied attributes of optical resources, viz., squeezed vacuum affinity (SVA) and Einstein-Podolsky-Rosen (EPR) correlation are necessary and/or sufficient for QT. The specific class of non-Gaussian resources that we have considered for this purpose are the two-mode entangled states generated by mixing nonclassical inputs with vacuum at the beam splitter (BS). Our analytical results show that SVA is not always nonzero and hence it cannot be considered to be a genuine attribute. Our numerical results show that there exist some BS-generated entangled states that do not give QT in spite of being EPR correlated, implying that EPR correlation is not sufficient for QT. In conjunction with the earlier observation in the literature to the effect that EPR correlation is not necessary for QT, our results lead to the conclusion that in general, EPR correlation is neither necessary nor sufficient for QT. Our results leave the question open as to what attributes, in general, may be necessary and/or sufficient for QT.

DOI
10.1103/physreva.103.032432

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Recent theoretical and experimental advances have demonstrated advantages of using non-Gaussian optical resources compared to the Gaussian ones in the context of quantum teleportation (QT), an important quantum information processing task. From both theoretical and experimental points of view the question of which attributes of the resources, besides entanglement, render them useful for QT is an important one. In this paper, we examine the question of whether two well-studied attributes of optical resources, viz., squeezed vacuum affinity (SVA) and Einstein-Podolsky-Rosen (EPR) correlation are necessary and/or sufficient for QT. The specific class of non-Gaussian resources that we have considered for this purpose are the two-mode entangled states generated by mixing nonclassical inputs with vacuum at the beam splitter (BS). Our analytical results show that SVA is not always nonzero and hence it cannot be considered to be a genuine attribute. Our numerical results show that there exist some BS-generated entangled states that do not give QT in spite of being EPR correlated, implying that EPR correlation is not sufficient for QT. In conjunction with the earlier observation in the literature to the effect that EPR correlation is not necessary for QT, our results lead to the conclusion that in general, EPR correlation is neither necessary nor sufficient for QT. Our results leave the question open as to what attributes, in general, may be necessary and/or sufficient for QT.
Non-Gaussian entangled states of light have been found to improve the success of quantum telepor- tation. Earlier works in the literature focussed mainly on two-mode non-Gaussian states generated by de-Gaussification of two-mode squeezed vacuum states. In the current work, we study quan- tum teleportation with a class of non-Gaussian entangled resource states that are generated at the output of a passive beam splitter (BS) with different input single mode non-Gaussian states. In particular, we consider input states that are generated under successive application of squeezing and photon addition/subtraction operations in various orders. We focus on identifying what attributes of the resource states are necessary or sufficient for quantum teleportation (QT). To this end we first evaluate two attributes considered in the literature, viz. squeezed vacuum affinity (SVA) and EPR correlation. While SVA is not non-zero for all two-mode resource states, EPR correlation is neither necessary nor sufficient of QT. We consider yet another attribute, viz. two-mode quadrature squeezing as defined by Simon et. al. [Phys. Rev. A 49, 1567 (1994)]. Our numerical results on the de-Gaussified two-mode squeezed vacuum state as well as the BS generated non-Gaussian states lead us to the conclusion that two-mode quadrature squeezing is a necessary condition for QT, in general. We further demonstrate the plausibility of this conclusion by giving an analytical proof that two-mode quadrature squeezing is a necessary condition for QT in the case of symmetric two-mode Gaussian resource states.
Abstract Quantum teleportation (QT) plays a central role in state-of-the-art information science and technology that necessitates proper characterization of the resources. While entanglement is known to be necessary, condition of sufficiency for QT still remains an open question. Here, we partially answer this question in light of Einstein-Podolsky-Rosen (EPR) correlation. In the case of input coherent state, we provide an analytic proof that with a general two-mode Gaussian entangled resources EPR correlation is sufficient for QT . For a relatively restricted set of Gaussian states, however bigger than that of the symmetric states, we further show that EPR correlation is both necessary and sufficient . On the other hand, in the case of Gaussian pure input, our numerical results hint that EPR correlation mostly appears to be a necessary condition only . However, the necessary and/or sufficient condition for QT of a Gaussian mixed input state, apart from the entanglement, still remains an open question.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter rrr and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter rrr.
Quantum teleportation (QT) lies at the heart of modern day quantum information science and technology. Despite extensive studies over past two decades, obtaining the necessary and/or sufficient criterion for QT with continuous-variable (CV) resources, besides entanglement, still remains an open concern. In this backdrop, here we analyze the role of a purely quantum optical (QO) attribute, known as quadrature squeezing, in CV teleportation. We first provide an analytic proof that for Gaussian resources quadrature squeezing is necessary for QT. However, for non-Gaussian resources we show a clear distinction between the pure and the mix states. For the pure states, quadrature squeezing appears to be necessary for QT, in the sense that there is no QT without quadrature squeezing. However, in the case of mix states we observe otherwise, i.e., QT could be achieved even without quadrature squeezing. Our results present the exotic character of the QO attributes of the CV resources and necessitate a deeper search for the necessary and/or sufficient criterion for CV QT.
In view of the increasing importance of non-Gaussian entangled states in quantum information protocols like teleportation and violations of Bell inequalities, the steering of continuous variable non-Gaussian entangled states is investigated. Einstein-Podolsky-Rosen steering for Gaussian states may be demonstrated through the violation of the Reid inequality involving products of the inferred variances of noncommuting observables. However, for arbitrary states the Reid inequality is not always necessary because of the higher-order correlations in such states. One then needs to use the entropic steering inequality. We examine several classes of currently important non-Gaussian entangled states, such as the two-dimensional harmonic oscillator, the photon-subtracted two-mode squeezed vacuum, and the NOON state, in order to demonstrate the steering property of such states. A comparative study of the violation of the Bell inequality for these states shows that the entanglement present is more easily revealed through steering compared to Bell violation for several such states.
In this work, we investigate the performance of non-Gaussian entangled resources in continuous-variable quantum teleportation within a realistic setting. We describe the characteristic functions of three distinct entangled resources, a two-mode squeezed vacuum state, a two-mode photon-subtracted squeezed state, and a two-mode photon-added squeezed state. We extend the theoretical analysis by Yang et al. to include the realistic experimental conditions such as photon losses, imperfect measurements which typically affect continuous-variable quantum teleportation. Our results demonstrate that even in non-ideal situations, the photon-subtracted squeezed state outperforms the other two resources in the low squeezing regime, keeping fidelity above the classical threshold that suggests the robustness of photon-subtracted squeezed state in practical teleportation applications. We further analyze the EPR correlations of these entangled resources, revealing that the photon-subtracted squeezed state exhibits stronger EPR correlations than the original two-mode squeezed vacuum state and the two-mode photon-added squeezed state. This study merges theoretical models with realistic imperfections and utilizes non-Gaussian entanglement into high-fidelity quantum teleportation.