Henrik Wilming

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Wilming

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Henrik

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0000-0002-0306-7679

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Publications 1 - 10 of 25

By-passing fluctuation theorems
Boes, Paul; Gallego, Rodrigo; Ng, Nelly H.Y.; et al. (2019)
arXiv
Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be violated if one allows for the use of catalysts - additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for statistical and quantum thermodynamics.
Von Neumann entropy from unitarity
Boes, Paul; Eisert, Jens; Gallego, Rodrigo; et al. (2018)
arXiv
Revivals imply quantum many-body scars
Alhambra, Álvaro M.; Anshu, Anurag; Wilming, Henrik (2020)
Physical Review B
Extensive Rényi entropies in matrix product states
Rolandi, Alberto; Wilming, Henrik (2020)
arXiv
We prove that all Rényi entanglement entropies of spin-chains described by generic (gapped), translational invariant matrix product states (MPS) are extensive for disconnected sub-systems: All Rényi entanglement entropy densities of the sub-system consisting of every k-th spin are non-zero in the thermodynamic limit if and only if the state does not converge to a product state in the thermodynamic limit. Furthermore, we provide explicit lower bounds to the entanglement entropy in terms of the expansion coefficient of the transfer operator of the MPS and spectral properties of its fixed point in canonical form. As side-result we obtain a lower bound for the expansion coefficient and singular value distribution of a primitve quantum channel in terms of its Kraus-rank and entropic properties of its fixed-point. For unital quantum channels this yields a very simple lower bound on the distribution of singular values and the expansion coefficient in terms of the Kraus-rank. Physically, our results are motivated by questions about equilibration in many-body localized systems, which we review.
Revisiting the equality conditions of the data-processing inequality for the sandwiched Renyi divergence
Wang, Jinzhao; Wilming, Henrik (2022)
Journal of Mathematical Physics
We provide a transparent, simple, and unified treatment of recent results on the equality conditions for the data-processing inequality of the sandwiched quantum Rényi divergence, including the statement that the equality in the data-processing implies recoverability via the Petz recovery map for the full range of the Rényi parameter α recently proven by Jenčová [J. Phys. A: Math. Theor. 50, 085303 (2017)]. We also obtain a new set of equality conditions, generalizing a previous result by Leditzky et al. [Lett. Math. Phys. 107, 61 (2017)].
Revivals imply quantum many-body scars
Alhambra, Álvaro M.; Wilming, Henrik (2019)
arXiv
We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time at most poly(N) implies the existence of "quantum many-body scars", whose number grows at least as the square root of N up to poly-logarithmic factors. These are energy eigenstates with energies placed in an equally-spaced ladder and with R\'enyi entanglement entropy scaling as log(N) plus an area law term for any region of the lattice. This shows that quantum many-body scars are a necessary condition for revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals, for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.
Operationally Meaningful Representations of Physical Systems in Neural Networks
Poulsen Nautrup, Hendrik; Metger, Tony; Iten, Raban; et al. (2020)
arXiv
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical structure present in the training data; however, these methods do not allow us to specify explicit and operationally meaningful requirements on the representation. Here, we present a neural network architecture based on the notion that agents dealing with different aspects of a physical system should be able to communicate relevant information as efficiently as possible to one another. This produces representations that separate different parameters which are useful for making statements about the physical system in different experimental settings. We present examples involving both classical and quantum physics. For instance, our architecture finds a compact representation of an arbitrary two-qubit system that separates local parameters from parameters describing quantum correlations. We further show that this method can be combined with reinforcement learning to enable representation learning within interactive scenarios where agents need to explore experimental settings to identify relevant variables.
Entropy and Reversible Catalysis
Wilming, Henrik (2021)
Physical Review Letters
I show that nondecreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst,"whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) catalytic entropy conjecture introduced by Boes et al. [Phys. Rev. Lett. 122, 210402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.210402]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.
Lieb-Robinson bounds imply locality of interactions
Wilming, Henrik; Werner, Albert H. (2020)
arXiv
Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviours as well as fermionic lattice models. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.
Finite Group Velocity Implies Locality of Interactions
Wilming, Henrik; Werner, Albert H. (2020)
arXiv
Spin systems with exponentially decaying k-body interactions have an effective finite group velocity for the propagation of correlations due to Lieb-Robinson bounds. We show that a finite group velocity conversely implies the locality of the underlying Hamiltonian: a system fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. Our result already follows from the behaviour of two-point correlation functions for single-site observables and generalizes to different decay behaviours. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for arbitrary bounded observables. In addition we show that our results generalize to fermionic lattice models.

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Henrik Wilming

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