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CRC Press eBooks

Fidelity and Information in the Quantum Teleportation of Continuous Variables

Takayoshi Kobayashi

Published Oct 15, 2025• 0 citations
Publisher

Abstract

Ideally, quantum teleportation should transfer a quantum state without distortion and without providing any information about that state. However, quantum teleportation of continuous electromagnetic-field variables introduces additional noise, limiting the fidelity of the quantum-state transfer. In this article, the operator describing the quantum-state transfer is derived. The transfer operator modifies the probability amplitudes of the quantum state in a shifted photon-number basis by enhancing low photon numbers and suppressing high photon numbers. This modification of the statistical weight corresponds to a measurement of finite resolution performed on the original quantum state. The limited fidelity of quantum teleportation is thus shown to be a direct consequence of the information obtained in the measurement.

DOI
10.1201/9781003618997-11

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Ideally, quantum teleportation should transfer a quantum state without distortion and without providing any information about that state. However, quantum teleportation of continuous electromagnetic-field variables introduces additional noise, limiting the fidelity of the quantum-state transfer. In this article, the operator describing the quantum-state transfer is derived. The transfer operator modifies the probability amplitudes of the quantum state in a shifted photon-number basis by enhancing low photon numbers and suppressing high photon numbers. This modification of the statistical weight corresponds to a measurement of finite resolution performed on the original quantum state. The limited fidelity of quantum teleportation is thus shown to be a direct consequence of the information obtained in the measurement.
Ideally, quantum teleportation should transfer a quantum state without distortion and without providing any information about that state. However, quantum teleportation of continuous electromagnetic-field variables introduces additional noise, limiting the fidelity of the quantum-state transfer. In this article, the operator describing the quantum-state transfer is derived. The transfer operator modifies the probability amplitudes of the quantum state in a shifted photon-number basis by enhancing low photon numbers and suppressing high photon numbers. This modification of the statistical weight corresponds to a measurement of finite resolution performed on the original quantum state. The limited fidelity of quantum teleportation is thus shown to be a direct consequence of the information obtained in the measurement.
We consider the teleportation of displaced Fock states which are highly non-classical states of the quantized electromagnetic field which have a set of remarkable quantum properties that include the peculiar oscillations of their photon number distributions. We use the transfer operator formalism to show that the quantum teleportation of a DFS renders a finite superposition of orthonormal DFS's and find its explicit mathematical expression in terms of the compression parameter of the correlated EPR states of the quantum channel. The expression for a teleported Fock state is also derived as a particular case of DFS's teleportation. We finally apply these results to study the fidelity of the teleportation of DFS's and the teleportation of their photon number statistics.
Quantum entanglement states in continuous-variable quantum teleportation can transfer any quantum state. However, errors occur in the quantum states before and after the transfer in scientific experiments because generating a perfect quantum entanglement is physically unattainable. This paper limits the quantum states transferred to squeezed coherent states and introduces a controller to classical information transfer in continuous-variable quantum teleportation to improve transfer accuracy. Under such a setup, we derived the optimal controller that maximizes the fidelity, independent of the measurement results and the value of the displacement of the squeezed coherent state.
Continuous-variable quantum teleportation enables deterministic teleportation of quantum states of optical modes. However, the state transfer is imperfect and limited by the amount of squeezing in the shared two-mode entangled state. Recently, it has been proposed and experimentally demonstrated that the performance of continuous-variable teleportation can be conditionally improved using a measurement-based noiseless quantum amplification [J. Zhao et al., Nat. Commun.14, 4745 (2023)10.1038/s41467-023-40438-z]. An inverse Gaussian filter with sufficiently high cut-off is applied to outcomes of the continuous-variable Bell measurement, which can increase the fidelity of state teleportation and the cost of making the protocol probabilistic. Here we provide a detailed theoretical analysis of this protocol and discuss its effects and limitations. We focus on teleportation of classes of Gaussian states with fixed covariance matrix and variable displacement. The measurement-based noiseless amplification conditionally improves the precision of estimation of the coherent displacement of the teleported state from the outcomes of continuous-variable Bell measurement. Therefore, more information about the teleported state is revealed and unity-gain teleportation becomes possible with a lower added thermal noise as compared to deterministic teleportation.