Related papers: Trace distance between fermionic Gaussian states f…
The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and…
This paper concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated…
We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global $U(1)$ symmetry. Using the Weingarten calculus, we derive analytical predictions for the non-Gaussianity,…
We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit…
We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) the diagonal entropy becomes equivalent to the…
The measures of distances between points in a Hilbert space are one of the basic theoretical concepts used to characterize properties of a quantum system with respect to some etalon state. These are not only used in studying fidelity of…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space…
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in…
The recently introduced Gaussian Process State (GPS) provides a highly flexible, compact and physically insightful representation of quantum many-body states based on ideas from the zoo of machine learning approaches. In this work, we give…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
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…
We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…