Can we accurately read or write quantum data?

TL;DR

The paper investigates whether reading and writing quantum data can be performed with perfect accuracy under fundamental physical constraints. It proves a no-go theorem: if the total Hamiltonian is bounded from below and the measurement process is isolated and unitary, accurate measurements and preparations of sharp observables are impossible. The argument extends from pure to mixed states via a density-operator formalism and relies on a reductio ad absurdum using the Hegerfeldt–Ruijsenaars lemma and calibration/pointer-persistence assumptions. The result strengthens existing no-go statements such as the Wigner-Araki-Yanase theorem and has broad implications for the feasibility and design of scalable quantum control, computing, and measurement-based technologies, while inviting consideration of alternative frameworks like unsharp observables.

Abstract

Applications of quantum mechanics rely on the accuracy of reading and writing data. This requires accurate measurements and preparations of the quantum states. I show that accurate measurements and preparations are impossible if the total Hamiltonian is bounded from below (as thought to be in our universe). This result invites a reevaluation of the limitations of quantum control, quantum computing, and other quantum technologies dependent on the accuracy of quantum preparations and measurements, and maybe of the assumption that the Hamiltonian is bounded from below.

Figures (1)

• Figure 1: The contradiction derived in the proof is that the pointer's ready state $\varphi_{\varnothing}$ has to be an eigenstate for both $\lambda$ and $\lambda'$, while in fact $\varphi_{\varnothing}$, $\varphi_{\lambda}$, and $\varphi_{\lambda'}$ have to be mutually orthogonal.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• proof : Justification
• Theorem 1
• proof
• Lemma 1: Hegerfeldt & Ruijsenaars
• Remark 1
• proof : Proof of Lemma \ref{['lemma:HegerfeldtRuijsenaars']}
• Theorem 2
• proof