Notes on Deterministic Programming of Quantum Observables and Channels

TL;DR

This paper investigates the fundamental limitations of deterministic quantum programming, establishing orthogonality constraints for programming different observables and channels, and providing bounds on multimeter efficiency.

Contribution

It generalizes the orthogonality result for quantum programming vectors and introduces size bounds for efficient quantum multimeters.

Findings

Programming vectors for different sharp observables are orthogonal without post-processing.

Different unitary channels also require orthogonal programming vectors.

Provides size bounds for efficient quantum programming devices.

Abstract

We study the limitations of deterministic programmability of quantum circuits, e.g., quantum computer. More precisely, we analyse the programming of quantum observables and channels via quantum multimeters. We show that the programming vectors for any two different sharp observables are necessarily orthogonal, whenever post-processing is not allowed. This result then directly implies that also any two different unitary channels require orthogonal programming vectors. This approach generalizes the well-known orthogonality result first proven by Nielsen and Chuang. In addition, we give size-bounds for a multimeter to be efficient in quantum programming.