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arXiv:2210.04531 · Physical Review A

Teleportation protocols with non-Gaussian operations: Conditional photon subtraction versus cubic phase gate

E. R. Zinatullin, S. B. Korolev, T. Yu. Golubeva

Published Feb 14, 2023• 12 citations
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Abstract

In our paper, we compare three teleportation protocols: The original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schr\"odinger cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.

DOI
10.1103/physreva.107.022422

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In our paper, we compare three teleportation protocols: The original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schr"odinger cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.
Quantum state engineering frequently employs non-Gaussian operations, particularly photon addition and subtraction, to tailor and improve the nonclassical characteristics of quantum states. We investigate how photon addition to a two-mode squeezed Fock state (TMSFS) influences its performance in the Braunstein-Kimble quantum teleportation protocol. We obtain the Wigner characteristic function of the photon-added TMSFS (PA-TMSFS) and evaluate the corresponding teleportation fidelities for both Gaussian and non-Gaussian input states. We further compare the teleportation performance of PA-TMSFS with that of its photon-subtracted counterpart by accessing their fidelity enhancements over the parent TMSFS and considering the probabilistic nature of both the operations. Our results demonstrate that photon subtraction provides superior teleportation performance compared with photon addition, with this advantage becoming more pronounced when the success probabilities of the corresponding non-Gaussian operations are considered. In particular, the symmetric (1,1)(1,1)(1,1) photon subtraction yields the optimal trade-off between teleportation fidelity and success probability among the configurations investigated. These findings highlight that photon subtraction retains its advantage even when the underlying entangled resource is already non-Gaussian.
In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from the single-mode squeezed vacuum state. We discuss two figures of merit for the teleportation process, (a) the fidelity, and (b) the maximum negativity of the Wigner function at the output. We elucidate how the non-Gaussian entangled resource lowers the requirements on the amount of squeezing necessary to achieve any given fidelity of teleportation, or to achieve negative values of the Wigner function at the output.
We propose a modified quantum teleportation scheme to increase the teleportation accuracy by applying a cubic phase gate to the displaced squeezed state. We describe the proposed scheme in the Heisenberg picture, evaluating it from the point of view of adding an error in teleportation, and show that it allows achieving less error than the original scheme. Repeating the description in the Schr\"odinger picture, we find the range of the displacement values at which our conclusions are valid. Using the example of teleportation of the vacuum state and the squeezed states, we show that the scheme allows one to achieve high-fidelity values.
The entanglement properties of non-Gaussian states are investigated, which are obtained by performing the photon addition, photon subtraction, photon-addition-then-subtraction, and photon-subtraction-then-addition operations on the two-mode squeezed vacuum state. We show that the partial von Neumann entropy of all the resulting states is greater than that of the original squeezed state, but only the photon-subtracted states and the photon-added-then-subtracted states have the stronger Einstein-Podolsky-Rosen correlation than the original squeezed state. Quantum teleportation of Braunstein and Kimble protocol is studied for coherent states, squeezed states, and mixed Gaussian states with the non-Gaussian entangled resources. For all the states to be teleported, the fidelity with the photon-subtracted and the photon-added-then-subtracted entangled resources is higher than that with the two-mode squeezed vacuum resource. Based on Bures fidelity, we find that quantum teleportation for mixed and classical single-mode Gaussian states is more faithful than for single-mode Gaussian states with high purity and nonclassicality.
Abstract We consider a practical scheme for the implementation of non-Gaussian operation, viz., photon subtraction, photon addition, and photon catalysis, on two-mode squeezed thermal state. The generated states are employed as resources in continuous-variable quantum teleportation. The results show that the three non-Gaussian operations can enhance the teleportation fidelity. Considering the success probability of the non-Gaussian operations, we identify single-photon catalysis and single photon subtraction to be optimal for teleporting input coherent states and squeezed vacuum states, at low and intermediate squeezing levels, respectively.
Non-Gaussian operations have been shown to enhance the fidelity of continuous-variable quantum teleportation. However, a disadvantage of these non-Gaussian operations is that they are probabilistic in nature. In this article we study the trade-off between teleportation fidelity and success probability for optimal performance of the teleportation protocol. To this end, we first derive a unified expression for the Wigner characteristic function describing three non-Gaussian states: photon-subtracted, photon-added, and photon-catalyzed two-mode squeezed vacuum states. We then utilize it to obtain the fidelity of teleportation for input coherent and squeezed vacuum states using the aforementioned non-Gaussian resource states. We optimize the product of the relative enhancement in fidelity and the probability of state preparation by tuning the transmissivity of the beam splitters involved in implementing non-Gaussian operations. This leads to a scenario that can be effectively implemented in a laboratory to enhance fidelity. It turns out that among all the non-Gaussian resource states considered, the symmetric one-photon-subtracted two-mode squeezed vacuum state is the most advantageous. We provide the associated optimal squeezing and beam splitter transmissivity values for the non-Gaussian resource states considered, which will be of significant interest to the experimental community. We also consider the effect of imperfect photon detectors on teleportation fidelity. Further, we expect the derived Wigner characteristic function to be useful in state characterization and other quantum information processing protocols.