Related papers: Recoverability from direct quantum correlations
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the…
Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability…
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $\rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the…
A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble…
We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases.…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
We investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
In this work, we present a multiple-scale perturbation technique suitable for the study of open quantum systems, which is easy to implement and in few iterative steps allows us to find excellent approximate solutions. For any time-local…
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…
The low-lying bound states of a microscopic quantum many-body system of $n$ particles and the related physical observables can be worked out in a truncated $n$--particle Hilbert space. We present here a non-perturbative analysis of this…
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
We introduce a general framework for detecting genuine multipartite entanglement and non full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement our…