Noisy quantum state redistribution with promise and the Alpha-bit

TL;DR

This paper extends quantum state redistribution to scenarios with one-sided promises and noisy channels, demonstrating how existing protocols can be combined to achieve capacities like the Alpha-bit, including entanglement-assisted classical communication.

Contribution

It introduces a method to handle one-sided promises in quantum state redistribution over noisy channels, reproduces known Alpha-bit capacities, and generalizes entanglement-assisted classical capacity using existing protocols.

Findings

Reproduces Alpha-bit capacities with known protocols.

Generalizes entanglement-assisted classical communication.

Shows quantum state redistribution protocols can simulate classical communication.

Abstract

We consider a variation of the well-studied quantum state redistribution task, in which the starting state is known only to the receiver Bob and not to the sender Alice. We refer to this as quantum state redistribution with a one-sided promise. In addition, we consider communication from Alice to Bob over a noisy channel $\mathcal{N}$, instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards the solution of this problem where we "embed" the promise as part of the state and then invoke known protocols for quantum state redistribution composed with known protocols for transfer of quantum information over noisy channels. Using our approach, we are able to reproduce the Alpha-bit capacities with or without entanglement assistance in Ref. [ArXiv:1706.09434], using known protocols for quantum state redistribution and quantum communication over noisy channels. Furthermore, we generalize the entanglement assisted classical Alpha-bit capacity, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.