Paul Gondolf
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View article: Quasi-optimal Sampling from Gibbs States via Non-commutative Optimal Transport Metrics
Quasi-optimal Sampling from Gibbs States via Non-commutative Optimal Transport Metrics Open
We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin …
View article: Continuity Bounds for Quantum Entropies Arising From a Fundamental Entropic Inequality
Continuity Bounds for Quantum Entropies Arising From a Fundamental Entropic Inequality Open
International audience
View article: Unified Framework for Continuity of Sandwiched Rényi Divergences
Unified Framework for Continuity of Sandwiched Rényi Divergences Open
In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched Rényi divergences such as the sandwiched Rényi conditional entropy. We follow three different approaches: The first one is the “almost addit…
View article: Energy preserving evolutions over Bosonic systems
Energy preserving evolutions over Bosonic systems Open
The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to …
View article: Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics Open
We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin …
View article: Continuity bounds for quantum entropies arising from a fundamental entropic inequality
Continuity bounds for quantum entropies arising from a fundamental entropic inequality Open
We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, $ρ_1$ and $ρ_2$. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the Jord…
View article: Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
Conditional Independence of 1D Gibbs States with Applications to Efficient Learning Open
We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We quantify this with alternative notions of the conditional mutual informat…
View article: Unified framework for continuity of sandwiched Rényi divergences
Unified framework for continuity of sandwiched Rényi divergences Open
In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched Rényi divergences such as the sandwiched Rényi conditional entropy. We follow three different approaches: The first one is the "almost addit…
View article: Energy preserving evolutions over Bosonic systems
Energy preserving evolutions over Bosonic systems Open
The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to …
View article: General Continuity Bounds for Quantum Relative Entropies
General Continuity Bounds for Quantum Relative Entropies Open
International audience
View article: Continuity of Quantum Entropic Quantities via Almost Convexity
Continuity of Quantum Entropic Quantities via Almost Convexity Open
International audience
View article: General Continuity Bounds for Quantum Relative Entropies
General Continuity Bounds for Quantum Relative Entropies Open
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
View article: Continuity of quantum entropic quantities via almost convexity
Continuity of quantum entropic quantities via almost convexity Open
Based on the proofs of the continuity of the conditional entropy by Alicki, Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF) method. This method allows us to prove a great variety of continuity bounds for the…