Super-Activation of Zero-Error Capacity of Noisy Quantum Channels

TL;DR

This paper demonstrates the super-activation of zero-error capacities in noisy quantum channels, showing that auxiliary resources like entanglement and feedback enable perfect communication where single uses fail.

Contribution

It introduces novel super-activation effects in quantum channels, revealing how entanglement and auxiliary resources enable zero-error communication beyond classical limitations.

Findings

Single-use quantum channels cannot transmit classical info perfectly, but two uses can via entanglement.

Assisted with noiseless qubits or entanglement, channels with zero classical capacity can transmit quantum info.

Classical feedback enables perfect transmission of classical and quantum info in channels with zero classical capacity.

Abstract

We study various super-activation effects in the following zero-error communication scenario: One sender wants to send classical or quantum information through a noisy quantum channel to one receiver with zero probability of error. First we show that there are quantum channels of which a single use is not able to transmit classical information perfectly yet two uses can. This is achieved by employing entangled input states between different uses of the given channel and thus cannot happen for classical channels. Second we exhibit a class of quantum channel with vanishing zero-error classical capacity such that when a noiseless qubit channel or one ebit shared entanglement are available, it can be used to transmit $\log_2 d$ noiseless qubits, where 2d is the dimension of input state space. Third we further construct quantum channels with vanishing zero-error classical capacity when assisted with classical feedback can be used to transmit both classical and quantum information perfectly. These striking findings not only indicate both the zero-error quantum and classical capacities of quantum channels satisfy a strong super-additivity beyond any classical channels, but also highlight the activation power of auxiliary physical resources in zero-error communication.