Universality cost of non-Gaussian enhancement in continuous-variable quantum teleportation: A fidelity--deviation trade-off

TL;DR

This paper investigates the trade-off between average fidelity and fidelity deviation in continuous-variable quantum teleportation, highlighting the universality cost of non-Gaussian enhancement and the importance of input uniformity.

Contribution

It introduces a framework to quantify the universality cost of non-Gaussian enhancement in CV teleportation using fidelity deviation and demonstrates the inherent trade-offs involved.

Findings

Deterministic unity-gain channels have zero fidelity deviation regardless of Gaussian or non-Gaussian resources.

Increasing average fidelity via input-selective conditioning generally raises fidelity deviation, indicating a universality cost.

Stronger filtering improves conditional fidelity but reduces success probability and input uniformity.

Abstract

Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.