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A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…
Quantum metrology aims to exploit many-body quantum states to achieve parameter-estimation precision beyond the standard quantum limit. For unitary parameter encoding generated by local Hamiltonians, such enhancement is characterized by…
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational…
Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a…
One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…
The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger…
We consider a multi-dimensional continuum Schr\"odinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper and a lower bound on the bipartite entanglement…
Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum…
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also…
The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition which lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of…
It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in…
The general solution to the quantum master equation (and its $Sp(2)$ symmetric counterpart) is constructed explicitly in case of finite number of variables. It is shown that the finite-dimensional solution is physically trivial and thus can…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition…
The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement…
We review methods that allow one to detect and characterise quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without…