Related papers: Realistic many-body quantum systems vs full random…
The von Neumann entropy of a $k$-body reduced density matrix $\gamma_k$ quantifies the entanglement between $k$ quantum particles and the remaining ones. In this short paper, we rigorously prove general properties of this entanglement…
The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs.…
We study quantum correlations and complexity of simulation, characterized by quantum mutual information and entanglement entropy in operator space respectively, for thermal states in critical, non-critical and quantum chaotic spin chains. A…
The quantum information approach to many body physics has been very successful in giving new insight and novel numerical methods. In these lecture notes we take a vertical view of the subject, starting from general concepts and at each step…
While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this work, we introduce an alternative…
We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
We construct upper bounds on entanglement entropies of many-body quantum states that have fixed energy expectation values with respect to geometrically local Hamiltonians. Our focus is on entanglement entropies of subsystems that make up…
We consider the dynamics of continuously measured many-body chaotic quantum systems. Focusing on the observable of state purification, we analytically describe the limits of strong and weak measurement rate, where in the latter case…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the…
The concept of concurrence is researched to characterize the dynamical behavior of the bipartite systems. The quantum kicked top model has great significance in the qubit systems and the chaotic properties of the entanglement. The…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum…