Quantum Speed Limits for Implementation of Unitary Transformations

TL;DR

This paper establishes fundamental speed limits for implementing unitary transformations in quantum systems, generalizing existing bounds and depending only on the target unitary's trace and the energy spectrum's characteristics.

Contribution

It introduces state-independent bounds on the speed of quantum unitary implementations, extending traditional quantum speed limits to a broader class of quantum operations.

Findings

Derived bounds depend only on the trace of the unitary and energy spectrum statistics.

Generalized Mandelstam-Tamm and Margolus-Levitin bounds for unitary implementation.

Applicable to various quantum information processing transformations.

Abstract

Quantum speed limits are the boundaries that define how quickly one quantum state can transform into another. Instead of focusing on the transformation between pairs of states, we provide bounds on the speed limit of quantum evolution by unitary operators in arbitrary dimensions. These do not depend on the initial and final state but depend only on the trace of the unitary operator that is to be implemented and the gross characteristics (average and variance) of the energy spectrum of the Hamiltonian which generates this unitary evolution. The bounds that we find can be thought of as the generalization of the Mandelstam-Tamm (TM) and the Margolus-Levitin (ML) bound for state transformations to implementations of unitary operators. We will discuss the application of these bounds in several classes of transformations that are of interest in quantum information processing.