Related papers: Entropy scaling law and the quantum marginal probl…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in…
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum…
We address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…
In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced…
We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
Entanglement patterns reveal essential information on many-body states and provide a way to classify quantum phases of matter. However, experimental studies of many-body entanglement remain scarce due to their unscalable nature. The present…
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…
The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs.…
We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
The quantum marginal problem consists in deciding whether a given set of marginal reductions is compatible with the existence of a global quantum state or not. In this work, we formulate the problem from the perspective of dynamical systems…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
We propose an approach to the realization of many-body quantum state distributions inspired by combined principles of thermodynamics and mesoscopic physics. Its essence is a maximum entropy principle conditioned by conservation laws. We go…
This work is concerned with the minimization of quantum entropies under local constraints of density, current, and energy. The problem arises in the work of Degond and Ringhofer about the derivation of quantum hydrodynamical models from…