Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations

TL;DR

This paper investigates the fundamental limitations of sequentially decomposing genuinely entangling quantum operations, revealing inherent fidelity gaps that cannot be eliminated, and introduces a variational protocol to quantify these gaps.

Contribution

It introduces a framework to analyze fidelity gaps in sequential decompositions of genuine entanglers and employs a variational method to quantify these gaps.

Findings

Fidelity gaps are inherent in sequential decompositions of genuine entanglers.

The gaps are independent of ancilla dimension and initial states.

A variational matrix-product-operator protocol effectively quantifies these gaps.

Abstract

We draw attention to the existence of "genuine" fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation in a one-way sequential recipe in which an ancillary system interacts locally and only once with each qubit in a row. Given the known "no-go" associated with such a theoretically and experimentally desirable decomposition, various figures of merit are introduced to analyze the optimal "fidelity" with which an arbitrary genuinely entangling operation may admit such a sequential decomposition. An efficient variational matrix-product-operator (VMPO) protocol is invoked in order to obtain numerically the minimal values of the fidelity gaps incurred upon sequential decomposition of genuine entanglers. We term the values of the gaps so obtained genuine in the light of possible connections to the concept of the genuine multipartite entanglement and since they are independent of the ancilla dimension and the initial states the associated unitaries act upon.