Storage and retrieval of von Neumann measurements

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 $N\to 1$ 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.

19 pages, 9 figures

References in corpus (6)

• Quantum-enhanced machine learning
• Asymptotic teleportation scheme as a universal programmable quantum processor
• Quantum teleportation scheme by selecting one of multiple output ports
• Optimal universal programming of unitary gates
• Programmability of covariant quantum channels
• Probabilistic storage and retrieval of qubit phase gates

Cited by in corpus (3)

• Universal adjointation of isometry operations using conversion of quantum supermaps
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• A resource theory of asynchronous quantum information processing