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We investigate multipartite entanglement for quantum states of 3d space geometry, described via generalised random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
Non-locality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Due to non-locality, mixed states of any two subsystems are correlated in a stronger way than what…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We study a special inhomogeneous quantum network consisting of a ring of $M$ pseudo-spins (here $M = 4$) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This…
We investigate the entanglement properties in a generalized quantum cluster model under periodic boundary condition. By evaluating the quantum conditional mutual information entropy under four subsystem partitions, we identify clear…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
We use complex network theory to study a class of continuous-variable quantum states that present both multipartite entanglement and non-Gaussian statistics. We consider the intermediate scale of several dozens of components at which such…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
The notion of typicality in statistical mechanics is essential to characterize a macroscopic system. An overwhelming majority of the pure state looks almost identical if we neglect macroscopic non-local correlations, suggesting that thermal…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
We show that the numerical strong disorder renormalization group algorithm (SDRG) of Hikihara et. al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with…
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…