# Performance analysis of d-dimensional quantum cryptography under state-dependent diffraction

## TL;DR

This paper investigates how diffraction affects high-dimensional quantum key distribution over long distances and proposes a pre-compensation method to mitigate state-dependent losses, enhancing security and key rates.

## Contribution

It introduces a pre-shaping protocol to counteract state-dependent diffraction effects in quantum cryptography, improving performance without compromising security.

## Key findings

- Pre-compensation reduces error rates caused by diffraction.
- The protocol improves secure key rates in long-distance QKD.
- Experimental results validate theoretical predictions.

## Abstract

Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a pre-compensation protocol based on pre-shaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, symbol-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain symbols to make the loss and phase shift of all states same. Our results show that the pre-compensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.