# Optimal quantum networks and one-shot entropies

arXiv: https://arxiv.org/abs/1606.02394 · HTML: https://mlsanity.com/paper/1606.02394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 1 of 1)

- [Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations](https://mlsanity.com/paper/2403.03761/) (2024)

## Abstract (arXiv)

We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interactive tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game.