Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles

TL;DR

This paper introduces a new framework to determine the exact maximum rotation angles achievable by noisy quantum dynamics, resulting in tight bounds on evolution time and highlighting fundamental differences from unitary dynamics.

Contribution

It provides the first exact maximum rotation angle bounds for noisy quantum dynamics using semi-definite programming, improving upon previous loose bounds.

Findings

Derived tight bounds on noisy quantum evolution time

Identified fundamental differences between noisy and unitary dynamics

Showed orthogonalization time is generally not applicable to noisy dynamics

Abstract

The laws of quantum physics place a limit on the speed of computation. In particular, the evolution time of a system from an initial state to a final state cannot be arbitrarily short. Bounds on the speed of evolution for unitary dynamics have long been studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, which are, however, not tight. In this paper, we present a new framework for quantum speed limit concerning noisy dynamics. Within this framework, we obtain the exact maximum rotation angle that noisy dynamics can achieve at any given time, which gives rise to a tight bound on the evolution time for noisy dynamics. The bound obtained through semi-definite programming highlights the fundamental differences between noisy dynamics and unitary dynamics. Furthermore, we show that the \textit{orthogonalization} time, defined as the minimum time required to evolve any initial state to a state with zero fidelity with respect to the initial state, is generally not applicable to noisy dynamics.