Related papers: Trace distance between fermionic Gaussian states f…
Genuine multimode entanglement in continuous variable systems can be quantified by exploring the geometry of the state-space, namely via the generalized geometric measure (GGM) which is defined as the shortest distance of a given multimode…
We numerically study the one-dimensional long-range Transverse Field Ising Model (TFIM) in the antiferromagnetic (AFM) regime at zero temperature using Generalized Hartree-Fock (GHF) theory. The spin-spin interaction extends to all spins in…
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
We present a general methodology for addressing the infinite hierarchy problem that arises in measurement-induced dynamics of replicated quantum systems. Our approach introduces trace-preserving replica cutoffs using tomographic-like…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
Quantum state tomography, aimed at deriving a classical description of an unknown state from measurement data, is a fundamental task in quantum physics. In this work, we analyse the ultimate achievable performance of tomography of…
The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem…
We propose a reliable entanglement measure for a two-mode squeezed thermal state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable states of the same kind. The requisite Uhlmann fidelity of a…
Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. We present a protocol that constrains quantum states by experimentally measured…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on…
This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…
This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and…