Can I read Storage and retrieval of von Neumann measurements on EtoBox?

Storage and retrieval of von Neumann measurements by Lewandowska, Paulina; Kukulski, Ryszard; Pawela, Łukasz; Puchała, Zbigniew is a scholarly article available to read on EtoBox.

What is Storage and retrieval of von Neumann measurements about?

This work examines the problem of learning an unknown von Neumann measurement of dimension $d$ from a finite number of copies. To obtain a faithful approximation of the given measurement we are allowed to use it $N$ times. Our main goal is to estimate the asymptotic behavior of the maximum value of the average fidelity function $F_d$ for a general $N \rightarrow 1$ learning scheme. We show that $F_d = 1 - \Theta\left(\frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. In addition to that, we compared various learning schemes for $d=2$. We observed that the learning scheme based on deterministic port-based teleportation is asymptotically optimal but performs poorly for low $N$. In particular, we discovered a parallel learning scheme, which despite its lack of asymptotic optimality, provides a high value of the fidelity for low values of $N$ and uses only two-qubit entangled memory states.

Author

Lewandowska, Paulina; Kukulski, Ryszard; Pawela, Łukasz; Puchała, Zbigniew

Published

2022

Language

EN