Binary search trees for generalized measurement

TL;DR

This paper introduces a method to implement generalized quantum measurements efficiently using a binary search tree approach, reducing resource requirements compared to traditional Neumark extension methods.

Contribution

It presents a novel binary search tree construction for generalized quantum measurements with logarithmic depth, enabling more resource-efficient experimental realization.

Findings

Binary search tree construction for measurements with logarithmic depth

Potential for experimental implementation via probe qubit coupling

Reduction in resource complexity compared to Neumark extension

Abstract

Generalized quantum measurements (POVMs or POMs) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of operations in an extended Hilbert space. For an arbitrary measurement, we show how to construct a binary search tree with a depth logarithmic in the number of possible outcomes. This could be implemented experimentally by coupling the measured quantum system to a probe qubit which is measured, and then iterating.