Communicating Properties of Quantum States over Classical Noisy Channels

TL;DR

This paper introduces STT-UEP, a novel protocol for efficiently transmitting quantum state properties over classical noisy channels by leveraging classical shadow tomography and unequal error protection, significantly reducing communication complexity.

Contribution

The paper presents a new protocol combining shadow tomography and unequal error protection to enable efficient quantum property transmission over noisy classical channels, with theoretical guarantees.

Findings

Achieves logarithmic scaling of communication complexity with the number of observables

Provides theoretical bounds on estimation accuracy based on channel error probability

Validated through numerical benchmarks demonstrating efficiency and accuracy

Abstract

Transmitting information about quantum states over classical noisy channels is an important problem with applications to science, computing, and sensing. This task, however, poses fundamental challenges due to the exponential scaling of state space with system size. We introduce shadow tomography-based transmission with unequal error protection (STT-UEP), a novel communication protocol that enables efficient transmission of properties of quantum states, allowing decoder-side estimation of arbitrary observables. Unlike conventional approaches requiring the transmission of a number of bits that is exponential in the number of qubits, STT-UEP achieves communication complexity that scales logarithmically with the number of observables, depending on the observable weight. The protocol exploits classical shadow tomography for measurement efficiency, and applies unequal error protection by encoding measurement bases with stronger channel codes than measurement outcomes. We provide theoretical guarantees on estimation accuracy as a function of the bit error probability of the classical channel, and validate the approach against several benchmarks via numerical results.