Implementation of quantum measurements using classical resources and only a single ancillary qubit

TL;DR

This paper introduces a resource-efficient method to implement general quantum measurements using only classical resources and a single ancillary qubit, with promising success probabilities and potential experimental advantages.

Contribution

The authors propose a novel probabilistic scheme for implementing POVMs with a single ancillary qubit, reducing resource overhead and demonstrating effectiveness for various measurement types.

Findings

Success probability exceeds a constant for typical rank-one Haar-random POVMs.

Numerical results show success probability above a constant for extremal POVMs up to dimension 1299.

Scheme potentially reduces noise in experimental realization compared to standard methods.

Abstract

We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension $d$ using only classical resources and a single ancillary qubit. Our method is based on the probabilistic implementation of $d$-outcome measurements which is followed by postselection of some of the received outcomes. We conjecture that the success probability of our scheme is larger than a constant independent of $d$ for all POVMs in dimension $d$. Crucially, this conjecture implies the possibility of realizing arbitrary nonadaptive quantum measurement protocol on a $d$-dimensional system using a single auxiliary qubit with only a \emph{constant} overhead in sampling complexity. We show that the conjecture holds for typical rank-one Haar-random POVMs in arbitrary dimensions. Furthermore, we carry out extensive numerical computations showing success probability above a constant for a variety of extremal POVMs, including SIC-POVMs in dimension up to 1299. Finally, we argue that our scheme can be favourable for the experimental realization of POVMs, as noise compounding in circuits required by our scheme is typically substantially lower than in the standard scheme that directly uses Naimark's dilation theorem.