Quantum Network Tomography with Multi-party State Distribution

TL;DR

This paper introduces Quantum Network Tomography, a method to characterize quantum channels in networks using end-to-end measurements, with solutions for star networks and insights into the benefits of pre-shared entanglement.

Contribution

It formulates the problem of quantum network tomography and provides polynomial sample complexity solutions for star networks with Pauli channels, highlighting entanglement advantages.

Findings

Polynomial sample complexity for star network tomography.

Pre-shared entanglement improves parameter identifiability.

Effective end-to-end estimation of quantum channel errors.

Abstract

The fragile nature of quantum information makes it practically impossible to completely isolate a quantum state from noise under quantum channel transmissions. Quantum networks are complex systems formed by the interconnection of quantum processing devices through quantum channels. In this context, characterizing how channels introduce noise in transmitted quantum states is of paramount importance. Precise descriptions of the error distributions introduced by non-unitary quantum channels can inform quantum error correction protocols to tailor operations for the particular error model. In addition, characterizing such errors by monitoring the network with end-to-end measurements enables end-nodes to infer the status of network links. In this work, we address the end-to-end characterization of quantum channels in a quantum network by introducing the problem of Quantum Network Tomography. The solution for this problem is an estimator for the probabilities that define a Kraus decomposition for all quantum channels in the network, using measurements performed exclusively in the end-nodes. We study this problem in detail for the case of arbitrary star quantum networks with quantum channels described by a single Pauli operator, like bit-flip quantum channels. We provide solutions for such networks with polynomial sample complexity. Our solutions provide evidence that pre-shared entanglement brings advantages for estimation in terms of the identifiability of parameters.