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Multipartite quantum states constitute the key resource for quantum computation. The understanding of their internal structure is thus of great importance in the field of quantum information. This paper aims at examining the structure of…
The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure…
Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited.…
A scheme to evaluate computation fidelities within the one-way model is developed and explored to understand the role of correlations in the quality of noisy quantum computations. The formalism is promptly applied to many computation…
A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which…
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing…
Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic…
In this work we developed a general approach to the problem of detecting and quantifying different kind of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely…
Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state…
Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…
Composite quantum systems can be in generic states characterized not only by entanglement, but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In…
This paper presents a new measure of entanglement which can be employed for multipartite entangled systems. The classification of multipartite entangled systems based on this measure is considered. Two approaches to applying this measure to…
Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the three-qubit case, the single residual…
Neural quantum states (NQS) have emerged as a powerful variational ansatz for representing quantum many-body wave functions. Their internal mechanisms, however, remain poorly understood. We investigate the role of correlations for NQS-like…
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary…
Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as Separable Neural Network Quantum States (SNNS), employs…