Superposition of Noisy Quantum Channels and Superactivation of Quantum Capacity: Theory and NMR experiments

Abstract

Coherence is an extremely valuable resource in quantum information theory. The coherent control of channels, whether over their temporal order or over the choice of channels, has been extensively studied for various advantages in quantum information and quantum communication. There even has been a long-standing tussle over which of these can even provide greater advantages. In this work, we introduce a different framework for achieving coherent control on the choice of trajectory - using a single ancillary register rather than two. We achieve this by superposing the corresponding Stinespring dilation unitaries for the Pauli channels, in particular the dephasing and depolarising channels. We arrive at conditions under which superposition generates a valid quantum channel. Using these, we superpose two dephasing channels and observe the occurrence of an interference pattern much like what happens when we superpose quantum states. Interestingly, we show that two dephasing channels can destructively interfere with each other, thereby effectively preserving the quantum coherence. Moreover, we superpose two zero-capacity channels in the form of entanglement-breaking channels to show that, within this framework, coherent control over the choice of trajectory can not only result in superactivation of quantum capacity, but also in its perfect activation. We experimentally verify the theoretical findings using nuclear magnetic resonance (NMR) techniques, thereby solidifying our claims.