More Entanglement Implies Higher Performance in Channel Discrimination Tasks

We show that every entangled state provides an advantage in ancilla-assisted bi- and multichannel discrimination that singles out its degree of entanglement, quantified in terms of the Schmidt number. The Schmidt-number robustness provides a compelling quantification of such an advantage, and, remarkably, the well-known robustness of entanglement exactly provides the largest multiplicative advantage an entangled state can provide compared to the case where no ancilla is used in a channel discrimination task.

Figure 1

The channel discrimination task that lower bounds the multiplicative advantage that an ancilla-system entangled state ${\rho }_{AS}$ can provide in channel discrimination. Time goes from left to right. Lines indicate quantum systems. The C-shaped box indicates the preparation of the state. The D-shaped box indicates the final arbitrary guessing measurement $M$. Boxes indicate quantum operations. The channels to be distinguished (dashed box) are a composition of a fixed channel $\mathrm{\Lambda }\in \mathcal{T}({\mathcal{H}}^S,{\mathcal{H}}^{S^{\prime }})$, tailored to ${\rho }_{AS}$, and of the generalized Pauli unitary rotations $X^m{Z}^n$.