Quantum Steganography over Noisy Channels: Achievability and Bounds

TL;DR

This paper develops an explicit quantum steganography encoding method for noisy channels, enabling secret communication by exploiting differences between the actual and perceived noise levels, and establishes bounds and optimality conditions.

Contribution

It introduces a new quantum steganography encoding scheme for noisy channels, analyzes its capacity, and proves its optimality for certain quantum codes, advancing secure quantum communication.

Findings

Encoding rate depends on channel noise parameters

The scheme is optimal for nondegenerate quantum codes

Secret key consumption rate is explicitly calculated

Abstract

Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for a sender, Alice, to hide a secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum channel that Eve believes to connect Alice and Bob. The actual physical channel connecting Alice and Bob is noisy, but less noisy than Eve believes. We show that for the bit-flip and depolarizing channels Alice can use Eve's lack of knowledge of the channel parameter to encode quantum information steganographically. We give an explicit encoding procedure and calculate the rate at which Alice and Bob can communicate secretly. We also show that our encoding is optimal for nondegenerate quantum codes. We calculate the rate at which secret key must be consumed. Finally, we discuss the possibility of steganographic communication over more general quantum channels, and conjecture a general formula for the steganographic rate.