Related papers: Geometrical structures of multipartite quantum sys…
We establish relations between Segre variety, conifold, Hopf fibration, and separable sets of pure two-qubit states. Moreover, we investigate the geometry and topology of separable sets of pure multi-qubit states based on a complex…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We investigate quantum steering for multipartite systems by using entropic uncertainty relations. We introduce entropic steering inequalities whose violation certifies the presence of different classes of multipartite steering. These…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
Recently, several hybrid approaches to quantum information emerged which utilize both continuous- and discrete-variable methods and resources at the same time. In this work, we investigate the bipartite hybrid entanglement between a…
Within the new description of the polarization structure of quantum light (given in Part I) some types of generalized coherent states related to the polarization SU(2) group are examined. With their help we give a quasiclassical description…
Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement…
Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We…
We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time…
The control over the geometry and topology of quantum systems is crucial for advancing novel quantum technologies. This work provides a synthesis of recent insights into the behaviour of quantum vortices within atomic Bose-Einstein…
A particularly simple description of separability of quantum states arises naturally in the setting of complex algebraic geometry, via the Segre embedding. This is a map describing how to take products of projective Hilbert spaces. In this…
A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC…