Speed-Accuracy Trade-Off Relations in Quantum Measurements and Computations

TL;DR

This paper establishes fundamental speed-accuracy trade-off relations in quantum measurements and computations, showing that zero-error implementations are impossible within finite time due to physical constraints like energy conservation and locality.

Contribution

It introduces universal speed-accuracy trade-off relations as no-go theorems for quantum measurements and computations, based on physical principles.

Findings

Zero-error quantum measurements cannot be completed in finite time for non-commutative operators.

Error-free quantum gate implementations changing energy cannot be achieved in finite time.

The relations serve as fundamental physical constraints applicable to various quantum operations.

Abstract

In practical measurements, it is widely recognized that reducing the measurement time leads to decreased accuracy. However, whether an inherent speed-accuracy trade-off exists as a fundamental physical constraint for quantum measurements is not obvious, and the answer remains unknown. Here, we establish a fundamental speed-accuracy trade-off relation based on the energy conservation law and the locality. Our trade-off works as a no-go theorem that the zero-error measurement for the operators that are non-commutative with the Hamiltonian cannot be implemented with finite time. This relation universally applies to various existing errors and disturbances defined for quantum measurements. We furthermore apply our methods to quantum computations and provide another speed-accuracy trade-off relation for unitary gate implementations, which works as another no-go theorem that any error-less implementations of quantum computation gates changing energy cannot be implemented with finite time, and a speed-disturbance trade-off for general quantum operations.