# Secret key distillation across a quantum wiretap channel under restricted eavesdropping

## TL;DR

This paper investigates secret key distillation over a quantum wiretap channel with realistic eavesdropping constraints, showing that key rates can surpass those achievable against an unrestricted eavesdropper, with implications for practical quantum communication.

## Contribution

It introduces a restricted eavesdropping model for quantum wiretap channels and demonstrates that key rates can exceed traditional capacities under these realistic conditions.

## Key findings

- Key rates can surpass capacities with restricted eavesdropping.
- Upper bounds on key rates are derived using relative entropy of entanglement.
- The model applies to free-space quantum optical communication scenarios.

## Abstract

The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Further, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, e.g., to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.