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

Understand

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.