Related papers: Reconstructing the whole from its parts
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…
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…
Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling…
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…
Provided a complete set of putative $k$-body reductions of a multipartite quantum state, can one determine if a joint state exists? We derive necessary conditions for this to be true. In contrast to what is known as the quantum marginal…
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 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…
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…
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,…
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…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…
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 examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
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…
We analyze the problem of reconstructing an unknown quantum state of a multipartite system from repeated measurements of local observables. In particular, via a system-theoretic observability analysis, we show that, even when the initial…
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 introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource R and…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…