Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory

Abstract

There exist memoryless zero-capacity quantum channels that when used jointly result in a channel with positive capacity. This phenomenon is called superactivation. Making use of Parrondo's paradox, we exhibit examples of the superactivation-like effect for the capacity of classical communication channels as well as quantum and private capacity of quantum channels with memory. There are several ingredients necessary for superactivation of quantum capacity to occur in the memoryless case. The first one is the requirement for the quantum channels which are suitable for superactivation to come from two distinct families: binding entanglement channels and erasure channels. The second one is the ability to utilize inputs which are entangled across the uses of the channels. Our construction uses a single family of erasure channels with classical memory to achieve the same superactivation-like effect for quantum capacity without any of the ingredients above.

Playing a true Parrondo's game with a three-state coin on a quantum walk

“…In Ref. [16] a super-activation-like effect for the capacity of classical as well as quantum communication channels with memory is constructed with the help of Parrondo's paradox. The previous attempt for a Parrondo's paradox with a single coin qubit on quantum walks failed in asymptotic limits [17,18].…”

Bounding Quantum Capacities via Partial Orders and Complementarity

“…Interestingly, the question whether the private capacity can be superactivated is still open, despite significant effort to find an answer [62,64,65]. Of course, the above corollary implies that if all regularized less noisy channels are also degradable, the private capacity cannot be superactivated.…”

Bounding quantum capacities via partial orders and complementarity

“…Interestingly, the question whether the private capacity can be superactivated is still open, despite significant effort to find an answer [34,50,53]. Of course, the above corollary implies that if all regularized less noisy channels are also degradable, the private capacity cannot be superactivated.…”