Entanglement cost of two-qubit orthogonal measurements

TL;DR

This paper numerically investigates the entanglement cost of generic two-qubit orthogonal measurements, revealing that it is generally higher than the average entanglement of their eigenstates, indicating a complex relationship between measurement nonseparability and eigenstate entanglement.

Contribution

The study provides the first numerical analysis of the entanglement cost for generic two-qubit orthogonal measurements, highlighting a gap between measurement nonseparability and eigenstate entanglement.

Findings

Entanglement cost exceeds average eigenstate entanglement in most cases.

Nonseparability of measurements is generally distinct from that of eigenstates.

Results suggest a complex relationship between measurement and eigenstate entanglement.

Abstract

The "entanglement cost" of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication. Here we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits. Our results strongly suggest that for almost all measurements of this kind, the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements, implying that the nonseparability of a two-qubit orthogonal measurement is generically distinct from the nonseparability of its eigenstates.