Related papers: Krylov complexity of density matrix operators
Coarse-graining a chaotic bistable oscillator into a binary symbol sequence is a standard reduction, but it often obscures the geometry of the reduced state space and structural constraints of physically meaningful stochastic evolution. We…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
Recently, Keating, Linden, and Wells \cite{KLW} showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
Nies and Scholz defined quantum Martin-L\"of randomness (q-MLR) for states (infinite qubitstrings). We define a notion of quantum Solovay randomness and show it to be equivalent to q-MLR using purely linear algebraic methods. Quantum…
We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry. Our approach combines the operator-algebra quantum error-correction (OAQEC) structure of…
We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubit-oscillator system. Using the generalized rotating wave approximation the reduced density matrices of the qubit and the oscillator are…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain…
Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a…
We derive a semiclassical approximation for the evolution generated by the Lindblad equation as a generalization of complex WKB theory. Linear coupling to the environment is assumed, but the Hamiltonian can be a general function of…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
We discuss the numerical solution methods available when solving for the steady-state density matrix of a time-independent open quantum optical system, where the system operators are expressed in a suitable basis representation as sparse…
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…