Quantum Speed Limits Based on Schatten Norms: Universality and Tightness

TL;DR

This paper introduces a universal framework for quantum speed limits based on Schatten norms, revealing their geometric interpretation, conditions for tightness, and applicability to qubit dynamics, thus advancing understanding of quantum evolution constraints.

Contribution

It develops a general class of quantum speed limits using Schatten norms, demonstrating their universality, tightness conditions, and geometric significance for qubit systems.

Findings

Geometric QSL is independent of Schatten norm for single-qubit states.

Existing speed limits are special cases of the Schatten norm-based class.

Geometric QSL is tighter for pure initial states in qubit dynamics.

Abstract

We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using Schatten $\alpha$-norms, firstly exploiting geometric features of the quantum state space, and secondly by applying the Holder's inequality for matrix norms. For single-qubit states, we find that the geometric QSL is independent of the chosen Schatten norm, thus revealing universality behavior. We compare these QSLs with existing speed limits in literature, showing that the latter results represent particular cases of a general class of QSLs related to Schatten $\alpha$-norms. We address necessary and sufficient conditions for the tightness of the QSLs that depends on populations and coherences of the qubits, also addressing their geometric meaning. We compare the QSLs obtained for qubit dynamics, also exploring their geometrical meaning. Finally, we show that the geometric QSL is tighter for general qubit dynamics with initial pure states, which indicates a universal QSL.