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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.…

Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…

Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge…

In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al. proposed a sufficient condition detecting the genuinely entangled pure states. In this paper, assume that a state with six non-zero coefficients is not a trivially…

This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…

It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has…

We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or…

Systems of four nonbinary particles, each having three or more internal states, exhibit maximally entangled states that are inaccessible to four qubits. This breaks the pattern of two- and three-particle systems, in which the existing graph…

Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a…

Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…

We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…

Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement…

The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of…

Entanglement is a key property of quantum states that acts as a resource for a wide range of tasks in quantum computing. Entanglement detection is a key conceptual and practical challenge. Without adaptive or joint measurements,…

In addition to being a workhorse for modern quantum technologies, entanglement plays a key role in fundamental tests of quantum mechanics. The entanglement of photons in multiple levels, or dimensions, explores the limits of how large an…

It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…

We introduce the challenges of multi-party quantum entanglement and explain a recent success in learning to take its measure. Given the widely accepted reputation of entanglement as a counter-intuitive feature of quantum theory, we first…