Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

TL;DR

This paper introduces an adaptive quantum state fidelity estimation method for bipartite higher-dimensional systems, utilizing local POVM measurements to produce tighter fidelity bounds for Bell-type entangled states.

Contribution

It presents a novel adaptive approach using state verifier operators constructed from local POVMs, improving fidelity estimation accuracy in higher-dimensional bipartite systems.

Findings

Constructed explicit state verifier operators for Bell-type states.

Derived tighter fidelity bounds than previous methods with additional measurements.

Demonstrated effectiveness in fewer measurement configurations.

Abstract

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et.al., Nature Physics (2018), 14, 1032~1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.