Optimality of programmable quantum measurements

Abstract

We prove that for a programmable measurement device that approximates every POVM with an error $\le \delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta }$. In the case of qubits we can improve the general result by showing a linear growth. This proves the optimality of the programmable measurement devices recently designed in [G. M. D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)].

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• Optimal universal programming of unitary gates
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• Programmability of covariant quantum channels
• Probabilistic storage and retrieval of qubit phase gates
• Infinite-Dimensional Programmable Quantum Processors
• Notes on Deterministic Programming of Quantum Observables and Channels
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Limitations on post-processing assisted quantum programming
• Port-Based State Preparation and Applications
• Quantum Advantage in Storage and Retrieval of Isometry Channels