Related papers: On Multiquantum Bits, Segre Embeddings and Coxeter…
The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the…
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any…
We investigate the geometrical structures of multipartite states based on construction of toric varieties. In particular, we describe pure quantum systems in terms of affine toric varieties and projective embedding of these varieties in…
Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
We construct quantum gate entangler for general multipartite states based on topological unitary operators. We show that these operators can entangle quantum states if they satisfy the separability condition that is given by the complex…
In this article we study forms of the Segre cubic over non-algebraically closed fields, their automorphism groups and equivariant birational rigidity. In particular, we show that all forms of the Segre cubic are cubic hypersurfaces and all…
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…
A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs…
These lecture notes are devoted to the recent progress in the geometric aspects of quantum integrable systems based on quantum groups solved using the Bethe ansatz technique. One part is devoted to their enumerative geometry realization…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Two qubits is the simplest system where the notions of separable and entangled states and entanglement witnesses first appear. We give a three dimensional geometric description of these notions. This description however carries no…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…
Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…
In contrast to abstract statistical analyses in the literature, we present a concrete physical diagrammatic model of entanglement characterization and measure with its underlying discrete phase-space physics. This paper serves as a…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…