Reduction Theory on the Relative Entropy-2-

Rodney W. Benoist, Jean-Paul Marchand, Walter Wyss

Martin Bodo Plenio, S. Virmani, Papadopoulos, P P

We introduce the theory of operator monotone functions and employ it toderive a new inequality relating the quantum relative entropy and the quantumconditional entropy. We present applications of this new inequality and inparticular we prove a new lower bound on the relative entropy of entanglementand other properties of entanglement measures.

Martin Bodo Plenio, S Virmani, P Papadopoulos

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and, in particular, we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.

Keye Martin

Yuya O. Nakagawa, Gábor Sárosi, Tomonori Ugajin

Graeme D. Berk, Simon Milz, Kavan Kishore Modi

In arXiv:2110.02613, we presented a generalised dynamical resource theory framework that enabled noise reduction techniques including dynamical decoupling (DD) to be studied. While this fundamental contribution remains correct, it has been found that the main resource quantifiers we employed to study these resource theories -- based on the relative entropies between Choi states of multitime processes -- are not monotonic under the allowed transformations. In this letter we detail modified relative entropy-based resource quantifiers, prove that they are indeed monotonic in our resource theories. We re-interpret our numerical results in terms of these new relative entropy monotones, arriving at the same empirical conclusions: DD can be understood as temporal resource distillation, and improvements to noise reduction via our multitimescale optimal dynamical decoupling (MODD) method coincide with a decrease in the corresponding non-Markovianity monotone.