Related papers: On the complexity of finding the maximum entropy c…
We address the problem of compressing density operators defined on a finite dimensional Hilbert space which assumes a tensor product decomposition. In particular, we look for an efficient procedure for learning the most likely density…
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…
Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which are necessary for the complete reconstruction of the most correlated states of…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
We consider the problem of optimal processing of quantum information at incomplete experimental data characterizing the quantum source. In particular, we then prove that for one-qubit quantum source the Jaynes principle offers a simple…
We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $\rho$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by…
We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm…
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…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…
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…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…