Entangled and sequential quantum protocols with dephasing

TL;DR

This paper demonstrates that dephasing quantum maps can be parallelized using entanglement, showing that entangled protocols are not more fragile or less effective than sequential ones under dephasing noise, with broad applicability across quantum theories.

Contribution

It extends the parallelization of quantum protocols to dephasing maps in arbitrary dimensions using tensor networks and string diagram transformations, applicable beyond standard quantum mechanics.

Findings

Entangled and sequential protocols are equally robust under dephasing noise.

Parallelization of dephasing maps does not compromise protocol effectiveness.

Results apply to various quantum theories via category-theoretic methods.

Abstract

Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in arbitrary dimension can also be parallelized. This implies that for general dephasing noise the protocol with entanglement is not more fragile than the corresponding sequential protocol and, conversely, the sequential protocol is not less effective than the entangled one. We derive this result using tensor networks. Furthermore, we only use transformations strictly valid within string diagrams in dagger compact closed categories. Therefore, they apply verbatim to other theories, such as geometric quantization and topological quantum field theory. This clarifies and characterizes to some extent the role of entanglement in general quantum theories.