Certifying quantumness with the classical fidelity threshold

TL;DR

This paper develops a method to certify the quantumness of channels using the classical fidelity threshold, reformulating existing protocols in terms of effective entanglement-braking channels to derive new bounds for qubit and coherent states.

Contribution

It introduces a reformulation of classical fidelity thresholds using effective entanglement-braking channels, enabling new certification protocols for quantum channels.

Findings

Derived deterministic and probabilistic CFTs for qubit states

Extended CFT framework to coherent states

Provided a unified approach to verify quantumness of channels

Abstract

For a given ensemble of input and target states, the classical fidelity threshold (CFT) is the maximum valve of the averaged fidelity, and it can be achieved with a measure-and-prepare operation. This quantity can be employed to verify whether the channel is in the quantum domain or not. In a recent work by Chiribella and Xie [Phys. Rev. Lett. {\bf 110}, 213601 (2013)], it was showed that all the information about the input and target states can be equivalently described by an entangled state and an effective entanglement-braking (EB) channel, and the CFTs can be defined with the Choi matrix of the effective EB channel. Following this idea, the protocol proposed by Fuchs and Sasaki [Quantum. Inf. Comput, {\bf 3}, 377 (2003)] are reformulated in terms of the effective EB channel, and ss applications, the deterministic and probabilistic CFTs for qubit states and the coherent states are derived in this paper.