Storage and retrieval of von Neumann measurements

• URL: http://arxiv.org/abs/2204.03029v2
• Date: Mon, 14 Nov 2022 19:11:52 GMT
• Title: Storage and retrieval of von Neumann measurements
• Authors: Paulina Lewandowska, Ryszard Kukulski, {\L}ukasz Pawela, Zbigniew Pucha{\l}a
• Abstract summary: This work examines the problem of learning an unknown von Neumann measurement of dimension $d$ from a finite number of copies. Our main goal is to estimate the behavior of the maximum value of the average fidelity function $F_d$ for a general $N rightarrow 1$ learning scheme.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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