Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem

TL;DR

This paper explores energy-constrained quantum channel discrimination, introduces new quantum speed limits for dynamical semigroups, and extends the Solovay-Kitaev theorem to Gaussian unitaries with energy considerations.

Contribution

It proves entanglement-free optimal discrimination, develops energy-constrained quantum speed limits, and generalizes the Solovay-Kitaev theorem to Gaussian unitaries with energy constraints.

Findings

Optimal EC discrimination does not require entanglement.

Finite parallel queries suffice for zero-error discrimination.

Gaussian Solovay-Kitaev theorem with energy-based approximation error.

Abstract

We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Ac\'in, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Secondly, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Thirdly, we establish a version of the Solovay--Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.