Storage and retrieval of von Neumann measurements via indefinite causal order structures
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929348331700224 |
|---|---|
| author | Lewandowska, Paulina Kukulski, Ryszard |
| author_facet | Lewandowska, Paulina Kukulski, Ryszard |
| contents | This work presents the problem of learning an unknown von Neumann measurement of dimension $d$ using indefinite causal structures. In the considered scenario, we have access to $N$ copies of the measurement. We use formalism of process matrices to store information about the given measurement, that later will be used to reproduce its best possible approximation. Our goal is to compute the maximum value of the average fidelity function $F_d(N)$ of our procedure. We prove that $F_d(N) = 1 - Θ\left( \frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. Furthermore, we present the SDP program for computing $F_d(N)$. Basing on the numerical investigation, we show that for the qubit von Neumann measurements using indefinite causal learning structures provide better approximation than quantum networks, starting from $N \ge 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11202 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Storage and retrieval of von Neumann measurements via indefinite causal order structures Lewandowska, Paulina Kukulski, Ryszard Quantum Physics This work presents the problem of learning an unknown von Neumann measurement of dimension $d$ using indefinite causal structures. In the considered scenario, we have access to $N$ copies of the measurement. We use formalism of process matrices to store information about the given measurement, that later will be used to reproduce its best possible approximation. Our goal is to compute the maximum value of the average fidelity function $F_d(N)$ of our procedure. We prove that $F_d(N) = 1 - Θ\left( \frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. Furthermore, we present the SDP program for computing $F_d(N)$. Basing on the numerical investigation, we show that for the qubit von Neumann measurements using indefinite causal learning structures provide better approximation than quantum networks, starting from $N \ge 3$. |
| title | Storage and retrieval of von Neumann measurements via indefinite causal order structures |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.11202 |