Entanglement Cost of Nonlocal Measurements

TL;DR

This paper investigates the entanglement resources needed for implementing certain nonlocal quantum measurements, providing bounds and exact values for specific classes of measurements, highlighting the relationship between measurement complexity and entanglement.

Contribution

It introduces bounds on the entanglement cost for orthogonal two-qubit measurements and identifies cases where the cost equals the average entanglement of eigenstates.

Findings

Upper and lower bounds on entanglement cost for certain measurements

Entanglement cost exceeds average eigenstate entanglement for most measurements

Exact entanglement cost equals average eigenstate entanglement for Pauli-invariant measurements

Abstract

For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.