Related papers: Markovian Marignals
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…
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…
The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several…
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 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…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
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…
Recently, we introduced a solution to the quantum marginal problem relevant to two-dimensional quantum many-body systems [I. H. Kim, Phys. Rev. X, 11, 021039]. One of the conditions was that the marginals are internally translationally…
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a canonical logarithmic construction $T(\mathcal R)$, the…
A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are…
Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…
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…
In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the…
The quantum marginal problem is concerned with characterizing which collections of quantum states on different subsystems are compatible in the sense that they are the marginals of some multipartite quantum state. Presented here is a…
We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…