Entanglement Dynamics Research Articles

Random unitaries, Robustness, and Complexity of Entanglement

It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints.

Boundary chaos: Exact entanglement dynamics

We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system’s boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases causes entanglement to grow on extensive time scales proportional to system size.

Exact entanglement dynamics of two spins in finite baths

Exact entanglement dynamics of two spins in finite baths

Conservation of acceleration and dynamic entanglement in mechanics

Conservation of acceleration and dynamic entanglement in mechanics

Measurement and Feedback Driven Entanglement Transition in the Probabilistic Control of Chaos.

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which the control is applied. We show that such control transitions persist in open quantum systems where control is implemented with local measurements and unitary feedback. Starting from a simple classical model with a known control transition, we define a quantum model that exhibits a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can also be probed by correlation functions without resolving individual quantum trajectories.

Weak ergodicity breaking in non-Hermitian many-body systems

The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.

Entanglement maintenance of classically pumped qubits and calibration aspects with the resonator tomography under the Stark shift effect inside a coherent resonator

We present a scheme for the investigation of entanglement of a similar qubits-pair along with the coherent resonator tomography under two-photon processes. Our discussion is focusing on the effect of the classical power amplitude along with Stark shift width and the conditions under which they have a constructive role in protecting the initial-state entanglement and the corresponding field tomography evolution. We observe that the entanglement between the qubits does maximally peak below a critical value and can be determined by suitable measurements on the resonator tomography. Interestingly, above the critical value, the tomography profile either shows an annular structure or exhibits quantumness which could be largely diminished by controlling the driving power intensity as well as the shift width. Particularly and for a detuned interaction, the critical values can be largely exceeded for sufficiently large values of the driving intensity and Stark shift, hence, more regions in the plane of parameters can be occupied by the qubits correlation. In this case, the pronounced fluctuations exhibited by entanglement dynamics due to phase variations could be highly interrupted. Additionally, preserving the field tomography showing a multi-component Schrödinger cat state via field-field detuning, robust, periodical and close to unity entanglement between the qubits could be highly possible. Moreover, in particular situations, the field tomography dynamics show the Fourier transform of the original field wave packet one-quarter period after initial, accordingly, entanglement maxima are reached frequently per a quarter period of rotation.

Entanglement propagation and dynamics in non-additive quantum systems

The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with a diverging contribution to the internal energy from the long-range two body potential. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.

Separable ball around any full-rank multipartite product state

We show that around any m-partite product state of full rank (that is , there exists a finite-sized closed ball of separable states centered around whose radius is . Here, is the smallest eigenvalue of . We are assuming that the total Hilbert space is finite dimensional and we use the notion of distance induced by the Frobenius norm. Applying a scaling relation, we also give a new and simple sufficient criterion for multipartite separability based on trace: . Using the separable balls around the full-rank product states, we discuss the existence and possible sizes of separable balls around any multipartite separable states, which are important features for the set of all separable states. We discuss the implication of these separable balls on entanglement dynamics.

Entanglement Dynamics Induced by a Three-Level Laser Coupled to the Squeezed Vacuum Reservoir

We have studied the squeezing and entanglement properties of the light induced by a three-level laser coupled to the squeezed vacuum reservoir. Applying the pertinent master equation, we have obtained the evolution equations for the cavity mode variables. Using the solutions of the resulting equations, the squeezing properties, entanglement amplification, and the normalized second-order correlation function of the cavity radiation are described. We have seen that the light generated by a three-level laser is in a squeezed state, and the squeezing occurs in the plus quadrature. In addition, we have also established that the effect of the squeezed parameter increases the mean and variance of the photon number. It is found that the squeezing and entanglement in the two-mode light are directly related. As a result, an increase in the degree of squeezing directly leads to an increase in the degree of entanglement and vice versa. This shows that, whenever there is squeezing in the two-mode light, there exists an entanglement in the system.

Thermal entanglement in two-atom Tavis–Cummings model with taking into account the dipole-dipole interaction

Background. Interest in the study of entangled states of systems of natural and artificial atoms (qubits) interacting with selected modes of microwave resonators is associated with their use as logic elements of quantum computers. At the same time, the most important task of the physics of quantum computing is the choice of the most effective mechanisms for manipulating and controlling the entangled states of qubits in such devices. Aim. The dynamics of the entanglement of two dipole-coupled superconducting Josephson qubits induced by a thermal noise of a coplanar resonator is studied for various initial states of the qubits. Methods. Based on the exact solution of the quantum Liouville equation for the whole density matrix of the system under consideration, the time behavior of the qubit entanglement parameter (negativity) is found for chaotic thermal, pure separable, and entangled initial states of qubits. Results. It is shown that the entanglement of qubits induced by the thermal noise of the resonator is possible for both the chaotic thermal states and separable states of qubits, except the case when both qubits are excited. It has also been found that, for small values of the dipole–dipole interaction parameter, taking this interaction into account leads to an increase in the degree of entanglement. For values of the dipole-dipole interaction parameter greater than some limit value, the opposite effect takes place. It is found that for entangled initial states of qubits, the inclusion of direct interaction has a small effect on the entanglement dynamics. It is shown that the initial coherence of qubit states can lead to a significant increase in the degree of their entanglement in the presence of a dipole–dipole interaction. Conclusion. The dipole-dipole interaction can be used as an effective mechanism for qubits entanglement manipulation and controlling.

Dynamics of a multipartite hybrid quantum system with beamsplitter, dipole–dipole, and Ising interactions

The possibility of exploiting heterogeneous quantum systems to high precision, for storing, processing, and transmitting information, makes them ideal candidates for multitasking purposes in quantum communication. Appropriate quantum systems involving a judicious choice of interactions that augment each other are potentially useful for probing deep into quantum regimes. Here, we use one such hybrid bipartite quantum model, with one subsystem made of a pair of qubits and another comprising a pair of oscillators, to study the entanglement dynamics and the entanglement transfer between discrete and continuous variables. The basic model is the standard double Jaynes–Cummings model, which, under suitable conditions, is known to support both entanglement transfer and entanglement sudden death. In this work, we generalize this model to include further experimentally relevant interactions, such as the beamsplitter-type exchange interaction between the oscillators, and dipole–dipole and Ising-type interactions between the qubits. The way various interactions and initial oscillator states affect the entanglement dynamics is examined theoretically for generic experimental conditions. Using exact analytical solutions, we show that, compared to the beamsplitter or dipole–dipole interaction, the Ising interaction can have a significant positive impact on entanglement sudden death and birth, and the postponement of the onset of these phenomena, apart from producing a substantial reduction in the time duration of the death.

The failure of Wigner function negativity to detect quantum dissonance in an open bipartite system

We study the dynamics of Wigner function, quantum discord, entanglement and quantum dissonance for bipartite Bell-diagonal states independently interacting with dephasing reservoirs. We analyze comparatively their behavior under the decoherence effect. Our main goal is to test the ability of Wigner function negativity to measure all kinds of quantum correlations in such system. Particularly, we find that this negativity can only capture entanglement and discord. Of course it succeeded in predicting the behavior of quantum dissonance, but nevertheless, it failed to detect its presence. As a matter of fact, we conclude that Wigner function negativity cannot be used as measure of quantum dissonance in the two qubit open system.

Enhancing the atomic correlation dynamics under the effects of Stark shift and Kerr medium through multi-photon transitions

Enhancing and preserving the atomic correlation and entanglement is of significant utility in quantum information. To this aim, we study the temporal evolution of uncertainty-induced nonlocality ([Formula: see text]) and logarithmic negativity ([Formula: see text]) as measures of quantum correlations (QCs) and quantum entanglement (QE) between two effective atoms coupled to a bosonic reservoir in the absence of thermal fluctuations and in the presence of Kerr medium (KM) and Stark shift (SS) under which n-photon transitions are permitted. We explore how Markovian and non-Markovian regimes affect the temporal dynamics of atomic correlation and entanglement and its limitations. Our findings indicate that by adjusting the KM and SS parameters, the quantum correlations between the two atoms can be enhanced and maintained while displaying similar qualitative behavior. Notably, it was observed that the QCs and QE quantities are at their highest magnitudes in the non-Markovian regime when the strengths of both SS and KM are increased, implying that QCs and QE are well protected. In contrast to the typical view that protecting the QCs from decoherence that may be observed owing to environmental noise, we proposed a gainful way to reduce the atomic decoherence by adjusting the number of n-photon transitions. Our investigation reveals that in the non-Markovian regime, the considered system exhibits better resistance against decoherence in comparison to the Markovian regime, as evidenced by the significant amount of quantum correlations detected among the two effective atoms at a specific point in time.

Effects of quantum quench on entanglement dynamics in antiferromagnetic Ising model

We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya (DM) interaction by using the quantum renormalization-group method and the definition of negativity. Two types of quench protocols (i) adding the DM interaction suddenly and (ii) rotating the spins around x axis are considered to drive the dynamics of the system, respectively. By comparing the behaviors of entanglement in both types of quench protocols, the effects of quench on dynamics of entanglement are studied. It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors. Especially, the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system. In addition, the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.

Frequency–modulated qubits in a dissipative cavity: entanglement dynamics and protection

Frequency–modulated qubits in a dissipative cavity: entanglement dynamics and protection

Enhancement of dynamical entanglement in a dispersive two-mode Jaynes–Cummings model via superposition of photon-added pair coherent state

In this paper, we introduce a new non-Gaussian state called superposition of photon-added pair coherent state (SPAPCS) by superposition addition of photons to two modes of a pair coherent state (PCS). It is demonstrated that the SPAPCS has an enhanced non-Gaussian property by testing its Wigner function when increasing the number of photons added to two modes of the PCS. We use the field as a SPAPCS to study a dynamical entanglement in a dispersive two-mode Jaynes–Cummings model in dissipation atom-field interaction. We detect the dynamical entanglement degrees of the global system and subsystems by using the linear entropy criteria. The obtained results show the dynamical entanglement degrees can be enhanced by the phase damping effect as well as the superposition adding photons to two modes of the field in SPAPCS.

Entanglement dynamics of multi-parametric random states: a single parametric formulation

A non-ergodic quantum state of a complex system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.

Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole

Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Here, we report a fermionic lattice-model-type realization of an analogue black hole by using a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behaviour of stimulated Hawking radiation, which is verified by the state tomography measurement of all 7 qubits outside the horizon. In addition, the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers.

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For -NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an -NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. -NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.