Related papers: Hilbert-space geometry of random-matrix eigenstate…
If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
In this work, we review different generalizations of the quantum geometric tensor (QGT) in two-band non-Hermitian systems and propose a protocol for measuring them in experiments. We present the generalized QGT components, i.e. the quantum…
This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic)…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of…
One of the methods proposed in the last years for studying non-perturbative gauge theory physics is quantum simulation, where lattice gauge theories are mapped onto quantum devices which can be built in the laboratory, or quantum computers.…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
Many-body localised phases of disordered, interacting quantum systems allow for exotic localisation protected quantum order in eigenstates at arbitrarily high energy densities. In this work, we analyse the manifestation of such order on the…
We investigate a family of quantum states defined by directed graphs, where the oriented edges represent interactions between ordered qubits. As a measure of entanglement, we adopt the Entanglement Distance - a quantity derived from the…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The…