Probing the qudit depolarizing channel

TL;DR

This paper compares different quantum probing schemes for the qudit depolarizing channel, showing that entanglement with an external ancilla generally offers the best information gain, especially when entanglement is inexpensive and well protected.

Contribution

It provides a comparative analysis of three channel identification schemes for qudit depolarizing channels, highlighting the advantages of entanglement, especially maximal entanglement, through analytical methods.

Findings

Entanglement with an ancilla often yields the most information per channel use.

Any amount of probe entanglement improves channel identification, with maximal entanglement being most beneficial.

Entanglement's advantage depends on its cost and shielding from depolarization.

Abstract

For the quantum depolarizing channel with any finite dimension, we compare three schemes for channel identification: unentangled probes, probes maximally entangled with an external ancilla, and maximally entangled probe pairs. This comparison includes cases where the ancilla is itself depolarizing and where the probe is circulated back through the channel before measurement. Compared on the basis of (quantum Fisher) information gained per channel use, we find broadly that entanglement with an ancilla dominates the other two schemes, but only if entanglement is cheap relative to the cost per channel use and only if the external ancilla is well shielded from depolarization. We arrive at these results by a relatively simple analytical means. A separate, more complicated analysis for partially entangled probes shows for the qudit depolarizing channel that any amount of probe entanglement is advantageous and that the greatest advantage comes with maximal entanglement.