Bounds in nonequilibrium quantum dynamics

Z Gong, R Hamazaki - International Journal of Modern Physics B, 2022‏ - World Scientific
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …

Maximal entanglement velocity implies dual unitarity

T Zhou, AW Harrow - Physical Review B, 2022‏ - APS
A global quantum quench can be modeled by a quantum circuit with local unitary gates. In
general, entanglement grows linearly at a rate given by entanglement velocity. Locality …

Entanglement rates and area laws

K Van Acoleyen, M Mariën, F Verstraete - Physical review letters, 2013‏ - APS
We prove an upper bound on the maximal rate at which a Hamiltonian interaction can
generate entanglement in a bipartite system. The scaling of this bound as a function of the …

Quantum skew divergence

KMR Audenaert - Journal of Mathematical Physics, 2014‏ - pubs.aip.org
In this paper, we study the quantum generalisation of the skew divergence, which is a
dissimilarity measure between distributions introduced by Lee in the context of natural …

Entanglement rates and the stability of the area law for the entanglement entropy

M Mariën, KMR Audenaert, K Van Acoleyen… - … in Mathematical Physics, 2016‏ - Springer
We prove a conjecture by Bravyi on an upper bound on entanglement rates of local
Hamiltonians. We then use this bound to prove the stability of the area law for the …

Entanglement rates for Rényi, Tsallis, and other entropies

A Vershynina - Journal of Mathematical Physics, 2019‏ - pubs.aip.org
We provide an upper bound on the maximal entropy rate at which the entropy of the
expected density operator of a given ensemble of two states changes under nonlocal unitary …

Bounds on Rényi entropy growth in many-body quantum systems

ZD Shi - Physical Review A, 2024‏ - APS
We prove rigorous bounds on the growth of α-Rényi entropies S α (t)(the von Neumann
entropy being the special case α= 1) associated with any subsystem A of a general lattice …

Entanglement rates for bipartite open systems

A Vershynina - Physical Review A, 2015‏ - APS
We provide an upper bound on the maximal rate at which irreversible quantum dynamics
can generate entanglement in a bipartite system. The generator of irreversible dynamics …

On bounding entangling rates and mixing rates in some special cases

Q Ning, FZ Guo, J Zhang, QY Wen - International Journal of Theoretical …, 2016‏ - Springer
We derive bounds on mixing rates in a special case when the probabilistic ensemble of
states is under certain restrictions. In this case we can prove the small incremental mixing …

[PDF][PDF] Quantum skew divergence: Theory and applications

KMR Audenaert - arxiv preprint arxiv:1304.5935, 2013‏ - researchgate.net
In this paper we study the quantum generalisation of the skew divergence, which is a
dissimilarity measure between distributions introduced by L. Lee in the context of natural …