Entanglement Negativity Research Articles

Tunable phonon-driven magnon–magnon entanglement at room temperature

We report the existence of entangled steady-states in bipartite quantum magnonic systems at elevated temperatures. We consider dissipative dynamics of two magnon modes in a bipartite antiferromagnet, subjected to interaction with a phonon mode and an external rotating magnetic field. To quantify the bipartite magnon–magnon entanglement, we use entanglement negativity and compute its dependence on temperature and magnetic field. We provide evidence that the coupling between magnon and phonon modes is necessary for the entanglement, and that, for any given phonon frequency and magnon–phonon coupling rate, there are always ranges of the magnetic field amplitudes and frequencies for which magnon–magnon entanglement persists at room temperature.

Detecting entanglement harnessing Lindblad structure

The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition, reduction map and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have defined a similar measure for genuine multipartite entanglement.

Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge

We utilize a holographic construction to compute the entanglement negativity for bipartite mixed state configurations of a single subsystem in CFTd s with a conserved charge dual to bulk geometries. In this context, we obtain the holographic entanglement negativity for single subsystems with long rectangular strip geometries in CFTd s with a conserved charge dual to bulk non extremal and extremal Reissner–Nordström (RN)- black holes at the leading order in a perturbation theory. We demonstrate that the holographic entanglement negativity computed involves the elimination of thermal contributions at the leading order confirming earlier results in the literature. This also conforms to quantum information theory expectations and constitutes further consistency checks for the holographic construction.

Random Tensor Networks with Non-trivial Links

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.

Towards a classification of holographic multi-partite entanglement measures

In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [1]. We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2d CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.

Coined quantum walks on the line: Disorder, entanglement, and localization.

Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the walker, we study how the localization affects the properties of the coined quantum walk. We find that the mixing properties of the walk are altered nontrivially with mixing being improved at short time scales. Special focus is given to the influence of coin disorder on the properties of the quantum state and the coin-walker entanglement. We find that disorder alters the quantum state significantly even when the walker probability distribution is still close to the nondisordered case. We observe that, generically, coin disorder decreases the coin-walker entanglement and that the localization leaves distinct traces in the entanglement entropy and the entanglement negativity of the coined quantum walk.

Channeling Quantum Criticality.

We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g function" in conformal field theory, allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the conformal field theory. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.

Decoherence, entanglement negativity, and circuit complexity for an open quantum system

In this paper, we compare the saturation time scales for complexity, linear entropy and entanglement negativity for two open quantum systems. Our first model is a coupled harmonic oscillator, where we treat one of the oscillators as the bath. The second one is a type of Caldeira Leggett model, where we consider a one-dimensional free scalar field as the bath. Using these open quantum systems, we discovered that both the complexity of purification and the complexity from operator state mapping is always saturated for a completely mixed state. More explicitly, the saturation time scale for both types of complexity is smaller than the saturation time scale for linear entropy. On top of this, we found that the saturation time scale for linear entropy and entanglement negativity is of the same order for the Caldeira Leggett model.

Entanglement negativity on random spin networks

We investigate multipartite entanglement for quantum states of $3D$ space geometry, described via generalized random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on entanglement negativity as a well defined witness of quantum correlations for mixed states, in our setting describing generic subregions of the boundary of a quantum $3D$ region of space. In particular, we consider a generic tripartition of the boundary of an open spin network state and we compute the typical R\'enyi negativity of two boundary subregions $A$ and $B$ immersed in the environment $C$, explicitly for a set of simple open random spin network states. We use the random character of the spin network to exploit replica and random average techniques to derive the typical R\'enyi negativty via a classical generalized Ising model correspondence generally used for random tensor networks in the large bond regime. For trivially correlated random spin network states, with only local entanglement between spins located on the network edges, we find that typical log negativity displays a holographic character, in agreement with the results for random tensor networks, in large spin limit. When nonlocal bulk entanglement between intertwiners at the vertices is considered the negativity increases, while at the same time the holographic scaling is generally perturbed by the bulk contribution.

Squashed entanglement in one-dimensional quantum matter

Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain structure of quantum systems. Building on this observation, we introduce the concept of quantum conditional mutual information between the edges of quantum many-body systems. We show that this quantity characterizes unambiguously one-dimensional topological insulators and superconductors, being equal to Bell-state entanglement in the former and to half Bell-state entanglement in the latter, mirroring the different statistics of the edge modes in the two systems. The edge-to-edge quantum conditional mutual information is robust in the presence of disorder or local perturbations, converges exponentially with the system size to a quantized topological invariant, even in the presence of interactions, and vanishes in the trivial phase. We thus conjecture that it coincides with the edge-to-edge squashed entanglement in the entire ground-state phase diagram of symmetry-protected topological systems, and we provide some analytical evidence supporting the claim. By comparing them with the entanglement negativity, we collect further indications that the quantum conditional mutual information and the squashed entanglement provide a very accurate characterization of nonlocal correlation patterns in one-dimensional quantum matter.

Mixed state information theoretic measures in boosted black brane

In this paper, we study various mixed state information theoretic quantities for a boosted black brane geometry. We have considered two setups, namely, a strip-like subsystem taken parallel and perpendicular to the direction of the boost. The quantities we calculate are the entanglement wedge cross-section, mutual information, entanglement negativity, and purification complexity. In the subsequent analysis, we have incorporated the thin-strip approximation and computed the leading order change (over pure AdS) in the concerned information theoretic quantities due to the boost parameter. We also show the relation of these quantities computed holographically to the energy and pressure of the boundary field theory. We then proceed to calculate the asymmetry ratios of these quantities, and observe that they are independent of the subsystem size. Finally, we proceed to study an interesting limit of the boosted black brane geometry, which is the so called AdS wave geometry. We once again compute all the mixed state information theoretic quantities for this geometry.

Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states

We use entanglement witnesses to detect entanglement in the XY chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We also consider a family of entanglement witnesses related to the entanglement negativity of the state. We test the witnesses in infinite and finite systems. We study how the temperature bounds obtained are influenced by a quantum phase-transition or a disorder line in the ground state. Very strong finite-size corrections are observed in the ordered phase due to the presence of a quasi-degenerate excitation. We also study the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. In the case of the Ising model, we find that the mixed postquench state is detected as entangled by the two methods if the parameters of the Hamiltonian before and after the quench are close to each other. We find that the two witnesses give qualitatively similar results, showing that energy-based entanglement witnesses are efficient in detecting the nearest-neighbor entanglement in spin chains in various circumstances. For other XY models, we find that the negativity based witnesses also detect states in some parameter regions where the energy-based witness does not, in particular, if the quench is performed from the paramagnetic phase to the ferromagnetic phase and vice versa. The domains in parameter space corresponding to postquench states detected as entangled by the energy-based witness have been determined analytically, which stresses further the utility of our method.

Entanglement negativity in a nonequilibrium steady state

We study entanglement properties in a nonequilibrium steady state of a free-fermion chain, that emerges after connecting two half-chains prepared at different temperatures. The entanglement negativity and the R\'enyi mutual information between two adjacent intervals scale logarithmically in the system size, with prefactors that we calculate analytically as a function of the bath temperatures. In particular, we show that the negativity and the R\'enyi mutual information with index $\ensuremath{\alpha}=1/2$ are described by different prefactors, and thus the two quantities provide inequivalent information about the state. Furthermore, we show that the logarithmic growth of the negativity during time evolution is also governed by the steady-state prefactor.

Entanglement negativity in a fermionic chain with dissipative defects: exact results

We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the Rényi mutual information with Rényi index , in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.

Entanglement dynamics of noisy random circuits

The process by which open quantum systems thermalize with an environment is both of fundamental interest and relevant to noisy quantum devices. As a minimal model of this process, we consider a qudit chain evolving under local random unitaries and local depolarization channels. After mapping to a statistical mechanics model, the depolarization (noise) acts like a symmetry-breaking field, and we argue that it causes the system to thermalize within a timescale independent of system size. We show that various bipartite entanglement measures---mutual information, operator entanglement, and entanglement negativity---grow at a speed proportional to the size of the bipartition boundary. As a result, these entanglement measures obey an area law: Their maximal value during the dynamics is bounded by the boundary instead of the volume. In contrast, if the depolarization only acts at the system boundary, then the maximum value of the entanglement measures obeys a volume law. We complement our analysis with scalable simulations involving Clifford gates, for both one- and two-dimensional systems.

Multipartite entanglement and purity dynamics in channels influenced by fractional Gaussian noise

The dynamical map of entanglement, coherence and mixedness in four-qubit maximally entangled GHZ-class state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement, coherence, and purity preservation may be simulated in multipartite GHZ-like states. Quantum correlations and purity decrease exponentially in four qubits, and exact fluctuating local field behavior, as well as entanglement sudden death and birth revivals, are completely suppressed. Entanglement, coherence, and purity preservation are affected by noise and the number of independent channels utilized. The Hurst parameter of fractional Gaussian noise was discovered in the four qubits to improve entanglement, coherence and avoid mixedness.

Quantumness of gravity in harmonically trapped particles

This study investigates the quantumness of gravity under the setup of the atomic interferometry from the viewpoint of mass-energy equivalence. We evaluated interference visibility considering a particle with internal energy levels in a harmonic trapping potential. As per the result, for a spatially superposed gravitational source mass, interference visibility exhibits collapse and revival behavior, which implies that an initial separable internal state evolves to the entangled state with respect to the degrees of freedom of the center of mass, the internal energy levels, and the external source state. In particular, it does not exhibit revival behavior when gravity is treated as a quantum interaction, while it revives with a finite period for a semiclassical treatment of gravity. We also examined the temporal behavior of entanglement negativity and found that the nonrevival behavior of visibility reflects the creation of the entanglement between the internal energy state and the external source state which is uniquely induced by the quantum interaction of gravity in accordance with the weak equivalence principle.

The transfer of entanglement negativity at the onset of interactions

Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement monotone negativity, we determine how the proclivity of an interaction to either generate, transfer or lose entanglement depends on the choice of Hamiltonians and initial states. These three proclivities are captured by Hamiltonian- and state-dependent quantities that we call negativity susceptibility, negativity transmissibility and negativity vulnerability respectively. These notions could serve, for example, as cost functions in quantum technologies such as machine-learned quantum error correction.

Symmetry-protected entanglement in random mixed states

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with ${\mathbb{Z}}_{N}$ and $\text{U}(1)$ symmetry groups. To this end, we develop a diagrammatic method to incorporate partial transpose within the random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries. We also design a quantum circuit to simulate our setup.

Entanglement Negativity and Concurrence in Some Low-Dimensional Spin Systems.

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed.