At the onset of an interaction between two initially independent systems, each system tends to experience an increase in its n-Renyi entropies, such as its von Neumann entropy (n = 1) and its mixedness (n = 2). We here ask which properties of a system determine how quickly its Renyi entropies increase and, therefore, how sensitive the system is to becoming entangled. We find that the rate at which the n-Renyi entropy increases in an interaction is determined by a quantity which we term the n-fragility of the system. The 2-fragility is closely related to the notion of 2-norm coherence, in that it too quantifies the extent to which a density matrix is off-diagonal with respect to the eigenbasis of a reference operator. Nevertheless, the 2-fragility is not a coherence monotone in the resource theoretic sense since it depends also on the eigenvalues of the reference operator. It is this additional sensitivity to the eigenvalues of the reference operator, here the interaction Hamiltonian, which enables the 2-fragility to quantify the rate of entropy production in interactions. We give an example using the light-matter interaction and we anticipate applications to the study of the rates at which two systems exchange classical and quantum information when starting to interact.
The occupancies and entropic entanglement measures for the ground state of two particles in a two-dimensional harmonic anisotropic trap are studied. We implement a method to study the large interaction strength limit for different short- and long-range interaction potentials that allows to obtain the exact entanglement spectrum and several entropies. We show that for long-range interactions, the von Neumann, min-entropy and the family of Rényi entropies remain finite for the anisotropic traps and diverge logarithmically for the isotropic traps. In the short-range interaction case the entanglem…
This communication is an enquiry into the circumstances under which entropy and subentropy methods can give an answer to the question of quantum entanglement in the composite state. Using a general quantum dynamical system we obtain the analytical solution when the atom initially starts from its excited state and the field in different initial states. Different features of the entanglement are investigated when the field is initially assumed to be in a coherent state, an even coherent state (Schrodinger cate state) and a statistical mixture of coherent states. Our results show that the setting…
In this work, we investigate the parameters governing the rate at which a quantum channel arises at the onset of an interaction between two systems, $A$ and $B$. In particular, when system $A$ is pre-entangled with an ancilla, $\tilde{A}$, we quantify the early-time transmission of pre-existing entanglement by calculating the leading order change in coherent information of the complementary channel ($A\rightarrow B'$). We show that, when $A$ and $B$ are initially unentangled and $B$ is pure, there is no change in coherent information to first order, while the leading (second) order change is d…
We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, an…
It has been increasingly becoming clear that Casimir and Casimir-Polder entropies may be negative in certain regions of temperature and separation. In fact, the occurrence of negative entropy seems to be a nearly ubiquitous phenomenon. This is most highlighted in the quantum vacuum interaction of a nanoparticle with a conducting plate or between two nanoparticles. It has been argued that this phenomenon does not violate physical intuition, since the total entropy, including the self-entropies of the plate and the nanoparticle, should be positive. New calculations, in fact, seem to bear this ou…
Negative entropy in connection with the Casimir effect at uniform temperature is a phenomenon rooted in the circumstance that one is describing a nonclosed system, or only part of a closed system. In this paper we show that the phenomenon is not necessarily restricted to electromagnetic theory, but can be derived from the quantum theory of interacting harmonic oscillators, most typically two oscillators interacting not directly but indirectly via a third one. There are two such models, actually analogous to the transverse magnetic (TM) and transverse electric (TE) modes in electrodynamics. The…
We study non-equilibrium processes in an isolated quantum system ---the Dicke model--- focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos and the excited-state quantum phase transition is more clear for the entanglemen…
We analyze the entanglement properties of the asymptotic steady state after a quench from free to hard-core bosons in one dimension. The Rényi and von Neumann entanglement entropies are found to be extensive, and the latter coincides with the thermodynamic entropy of the Generalized Gibbs Ensemble (GGE). Computing the spectrum of the two-point function, we provide exact analytical results both for the leading extensive parts and the subleading terms for the entropies as well as for the cumulants of the particle number fluctuations. We also compare the extensive part of the entanglement entropy…
Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically pol…
We summarize our recent results for the induced exchange interaction due to thermal bosonic environment (bath) which also generates quantum noise. Our focus here is on the onset of the interaction. We demonstrate that the induced interaction can be used to manipulate and create entanglement over time scales sufficiently large for controlling the two-qubit system for quantum computing applications, though ultimately the noise effects will dominate.
The growth of Renyi entropies after the injection of energy into a correlated system provides a window upon the dynamics of its entanglement properties. We develop here a simulation scheme by which this growth can be determined in Luttinger liquids systems with arbitrary interactions, even those introducing gaps into the liquid. We apply this scheme to an experimentally relevant quench in the sine-Gordon field theory. While for short times we provide an analytic expression for the growth of the second and third Renyi entropy, to access longer times, we combine our scheme with truncated spectru…
We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of $N=10$ interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrödinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify …
We characterize non-perturbatively the Rényi entropies of degree n=2,3,4, and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit. We carry out our calculations using lattice methods devised recently by us. Our results show the effect of strong pairing correlations on the entanglement entropy, which modify the sub-leading behavior for large subsystem sizes (as characterized by the dimensionless parameter x=kF L_A, where kF is the Fermi momentum and L_A the linear subsystem …
We perform quantum Monte Carlo calculations to determine how the Renyi entropies, $S_n$, of the interacting Fermi liquid depend on Renyi order, $n$, and scale as a function of system size, $L$. Using the swap operator and an accurate Slater-Jastrow wave function, we compute Renyi entropies for spinless fermions interacting via the Coulomb and modified Pöschl-Teller potentials across a range of correlation strengths. Our results show that interactions increase the Renyi entropies and increase the prefactor of their scaling laws. The relationships between Renyi entropies of different order $n$ a…
The entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength. Excellent measures for this purpose are the von-Neumann entropy, Havrda-Charv{\' a}t-Tsallis entropies, and the averaged inverse participation ratio. All the entropies are shown to follow a remarkably simple exponential form, which describes a universal and rapid transition to nearly maximal entanglement for increasing interaction strength. An unexpectedly exact relationship between the subsystem averaged inverse participation ratio and purity is derived that…
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate re-scaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the non-perturbative regime is performed using a recursively …
We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson b…
We investigate the crossover of the entanglement entropy towards its thermal value in nearly integrable systems. We employ equation of motion techniques to study the entanglement dynamics in a lattice model of weakly interacting spinless fermions after a quantum quench. For weak enough interactions we observe a two-step relaxation of the entanglement entropies of finite subsystems. Initially the entropies follow a nearly integrable evolution, approaching the value predicted by the Generalized Gibbs Ensemble (GGE) of the unperturbed model. Then, they start a slow drift towards the thermal stati…
We show, using an ab initio approach based on Quantum Monte Carlo technique, that the pseudogap regime emerges in ultracold Fermi gases close to the unitary point. We locate the onset of this regime at a value of the interaction strength corresponding to (k_{F}a)^{-1}\approx -0.05 (a - scattering length). We determine the evolution of the gap as a function of temperature and interaction strength in the Fermi gas around the unitary limit and show that our results exhibit a remarkable agreement with the recent wave-vector resolved radio frequency spectroscopy data. Our results indicate that a fi…
We study the properties of spectra and eigenfunctions for a chain of $1/2- $spins (qubits) in an external time-dependent magnetic field, and under the conditions of non-selective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transition and show that for the interaction between nearest qubits, the transition is very different from that to quantum chaos. We explain this phenomena by showing that in the considered region of parameters …
We prove rigorous bounds on the growth of $α$-Renyi entropies $S_α(t)$ (the Von Neumann entropy being the special case $α= 1$) associated with any subsystem $A$ of a general lattice quantum many-body system with finite onsite Hilbert space dimension. For completely non-local Hamiltonians, we show that the instantaneous growth rates $|S'_α(t)|$ (with $α\neq 1$) can be exponentially larger than $|S'_1(t)|$ as a function of the subsystem size $|A|$. For $D$-dimensional systems with geometric locality, we prove bounds on $|S'_α(t)|$ that depend on the decay rate of interactions with distance. When…
The time evolution of the entanglement entropy is a key concept to understand the structure of a non-equilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a…
