Measure Of Entanglement Research Articles

Entanglement wedge cross-section with Gauss-Bonnet corrections and thermal quench

The entanglement wedge cross section (EWCS) is numerically investigated statically and dynamically in a five-dimension AdS-Vaidya spacetime with Gauss-Bonnet (GB) corrections, focusing on two identical rectangular strips on the boundary. In the static case, EWCS increases as the GB coupling constant $\alpha$ increases and disentangles at small separation between two strips for smaller $\alpha$. For the dynamic case, such a monotonic relationship between EWCS and $\alpha$ holds but the two strips no longer disentangle monotonically as in the static case. In the early thermal quenching stage, the disentanglement occurs at smaller $\alpha$ with larger separations. Two strips then disentangle at larger {separation} with larger $\alpha$ as time evolves. Our results indicate that the higher-order derivative corrections, like the entanglement measure in the dual boundary theory, also have nontrivial effects on the EWCS evolution.

Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer

Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of a qubit with other qubits is found for the graph states represented by arbitrary graphs. The entanglement depends on the degree of the vertex representing the qubit, the absolute values of the parameter of the phase shift gate and the parameter of state the gate is acting on. Also the geometric measure of entanglement of the graph states is quantified on the quantum computer . The results obtained on the quantum device are in good agreement with analytical ones.

Witnessing pairing correlations in identical-particle systems

Quantum correlations and entanglement in identical-particle systems have been a puzzling question which has attracted vast interest and widely different approaches. Witness formalism developed first for entanglement measurement can be adopted to other kind of correlations. An approach is introduced by Kraus \emph{et al.}, [Phys. Rev. A \textbf{79}, 012306 (2009)] based on pairing correlations in fermionic systems and the use of witness formalism to detect pairing. In this contribution, a two-particle-annihilation operator is used for constructing a two-particle observable as a candidate witness for pairing correlations of both fermionic and bosonic systems. The corresponding separability bounds are also obtained. Two different types of separability definition are introduced for bosonic systems and the separability bounds associated with each type are discussed.

Geometric quantification of multiparty entanglement through orthogonality of vectors

The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the subsystems. Here, we demonstrate the geometrical conditions of the post-measurement vectors which maximize the entanglement corresponding to the bi-partitions and can yield non-identical set of maximally entangled states. The Bell states for the two qubit case, GHZ and GHZ like states with superposition of four constituents for three qubits, naturally arise as the maximally entangled states. The geometric conditions for maximally entangled two qudit systems are derived, leading to the generalised Bell states, where the reduced density matrices are maximally mixed. We further show that the reduced density matrix for an arbitrary finite dimensional subsystem of a general qudit state can be constructed from the overlap of the post-measurement vectors. Using this approach, we discuss the trade-off between the local properties namely predictability and coherence with the global property, entanglement for the non-maximally entangled two qubit state.

Entanglement measures in a nonequilibrium steady state: Exact results in one dimension

Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics. However, exact analytical results remain scarce, especially for systems out of equilibrium. In this work we examine a paradigmatic one-dimensional fermionic system that consists of a uniform tight-binding chain with an arbitrary scattering region near its center, which is subject to a DC bias voltage at zero temperature. The system is thus held in a current-carrying nonequilibrium steady state, which can nevertheless be described by a pure quantum state. Using a generalization of the Fisher-Hartwig conjecture, we present an exact calculation of the bipartite entanglement entropy of a subsystem with its complement, and show that the scaling of entanglement with the length of the subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term. The linear term is related to imperfect transmission due to scattering, and provides a generalization of the Levitov-Lesovik full counting statistics formula. The logarithmic term arises from the Fermi discontinuities in the distribution function. Our analysis also produces an exact expression for the particle-number-resolved entanglement. We find that although to leading order entanglement equipartition applies, the first term breaking it grows with the size of the subsystem, a novel behavior not observed in previously studied systems. We apply our general results to a concrete model of a tight-binding chain with a single impurity site, and show that the analytical expressions are in good agreement with numerical calculations. The analytical results are further generalized to accommodate the case of multiple scattering regions.

Universal Limitations on Quantum Key Distribution over a Network

We consider the distribution of secret keys, both in a bipartite and a multipartite (conference) setting, via a quantum network and establish a framework to obtain bounds on the achievable rates. We show that any multipartite private state--the output of a protocol distilling secret key among the trusted parties--has to be genuinely multipartite entangled. In order to describe general network settings, we introduce a multiplex quantum channel, which links an arbitrary number of parties, where each party can take the role of sender only, receiver only, or both sender and receiver. We define asymptotic and non-asymptotic LOCC-assisted secret-key-agreement (SKA) capacities for multiplex quantum channels and provide strong and weak converse bounds. The structure of the protocols we consider, manifested by an adaptive strategy of secret key and entanglement [Greenberger-Horne-Zeilinger (GHZ state)] distillation over an arbitrary multiplex quantum channel, is generic. As a result, our approach also allows us to study the performance of quantum key repeaters and measurement-device-independent quantum key distribution (MDI-QKD) setups. For teleportation-covariant multiplex quantum channels, we get upper bounds on the SKA capacities in terms of the entanglement measures of their Choi states. We also obtain bounds on the rates at which secret key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. We are able to determine the capacities for MDI-QKD setups and rates of GHZ-state distillation for some cases of interest.

Toward witnessing molecular exciton entanglement from spectroscopy

Entanglement is a defining feature of quantum mechanics that can be a resource in engineered and natural systems, but measuring entanglement in experiment remains elusive especially for large chemical systems. Most practical approaches require determining and measuring a suitable entanglement witness which provides some level of information about the entanglement structure of the probed state. A fundamental quantity of quantum metrology is the quantum Fisher information (QFI) which is a rigorous witness of multipartite entanglement that can be evaluated from linear response functions for certain states. In this work, we explore measuring the QFI of molecular exciton states of the first-excitation subspace from spectroscopy. In particular, we utilize the fact that the linear response of a pure state subject to a weak electric field over all possible driving frequencies encodes the variance of the collective dipole moment in the probed state, which is a valid measure for QFI. The systems that are investigated include the molecular dimer, $N$-site linear aggregate with nearest-neighbor coupling, and $N$-site circular aggregate, all modeled as a collection of interacting qubits. Our theoretical analysis shows that the variance of the collective dipole moment in the brightest dipole-allowed eigenstate is the maximum QFI. The optical response of a thermally equilibrated state in the first-excitation subspace is also a valid QFI. Theoretical predictions of the measured QFI for realistic linear dye aggregates as a function of temperature and energetic disorder due to static variations of the host matrix show that 2- to 3-partite entanglement is realizable. This work lays some groundwork and inspires measurement of multipartite entanglement of molecular excitons with ultrafast pump-probe experiments.

Tighter constraints of multiqubit entanglement in terms of unified entropy

We present classes of monogamy inequalities related to the αth () power of the entanglement measure based on the unified-() entropy, and polygamy inequalities related to the βth () power of the unified-() entanglement of assistance by using Hamming weight. We show that these monogamy and polygamy inequalities are tighter than the existing ones. Detailed examples are given for illustrating the advantages.

Moments of quantum purity and biorthogonal polynomial recurrence

The Bures–Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures–Hall ensemble as measured by the simplest form of an entanglement measure—the quantum purity. The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions, where the corresponding results in the literature are limited to the scenario of equal subsystem dimensions. In obtaining the results, we have derived recurrence relations of the underlying integrals over the Cauchy–Laguerre biorthogonal polynomials that may be of independent interest.

Polarization-insensitive interferometer based on a hybrid integrated planar light-wave circuit

Interferometers are essential elements in classical and quantum optical systems. The strictly required stability when extracting the phase of photons is vulnerable to polarization variation and phase shift induced by environment disturbance. Here, we implement polarization-insensitive interferometers by combining silica planar light-wave circuit chips and Faraday rotator mirrors. Two asymmetric interferometers with temperature controllers are connected in series to evaluate the single-photon interference. Average interference visibility over 12 h is above 99%, and the variations are less than 0.5%, even with active random polarization disturbance. The experiment results verify that the hybrid chip is available for high-demand applications like quantum key distribution and entanglement measurement.

Managing the three-party entanglement challenge

We introduce the challenges of multi-party quantum entanglement and explain a recent success in learning to take its measure. Given the widely accepted reputation of entanglement as a counter-intuitive feature of quantum theory, we first describe pure-state entanglement itself. We restrict attention to multi-party qubit states. Then we introduce the features that have made it challenging for several decades to extend an entanglement measure beyond the 2-qubit case of Bell states. We finish with a description of the current understanding that solves the 3-qubit entanglement challenge. This necessarily takes into account the fundamental division of the 3-qubit state space into two completely independent sectors identified with the so-called GHZ and W states.

Monogamy of entanglement measures based on fidelity in multiqubit systems

We show exactly that the $\alpha$th power of Bures measure of entanglement and geometric measure of entanglement, as special case of entanglement measures based on fidelity, obey a class of general monogamy inequalities in an arbitrary multiqubit mixed state for $\alpha\geq1$.

Simple sufficient condition for subspace to be completely or genuinely entangled

We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the d-level Dicke states.

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.

Simple mitigation of global depolarizing errors in quantum simulations.

To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.

Gaussian continuous-variable isotropic state

Inspired by the definition of the non-Gaussian two-parametric continuous variable analogue of an isotropic state introduced by Mi\v{s}ta et al. [Phys. Rev. A, 65, 062315 (2002); arXiv:quant-ph/0112062], we propose to take the Gaussian part of this state as an independent state by itself, which yields a simple, but with respect to the correlation structure interesting example of a two-mode Gaussian analogue of an isotropic state. Unlike conventional isotropic states which are defined as a convex combination of a thermal and an entangled density operator, the Gaussian version studied here is defined by a convex combination of the corresponding covariance matrices and can be understood as entangled pure state with additional Gaussian noise controlled by a mixing probability. Using various entanglement criteria and measures, we study the non-classical correlations contained in this state. Unlike the previously studied non-Gaussian two-parametric isotropic state, the Gaussian state considered here features a finite threshold in the parameter space where entanglement sets in. In particular, it turns out that it exhibits an analogous phenomenology as the finite-dimensional two-qubit isotropic state.

Computable and Operationally Meaningful Multipartite Entanglement Measures.

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state |ψ⟩ for these applications is often directly related to the degree or type of entanglement present in |ψ⟩. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

Disentangling (2+1)D topological states of matter with entanglement negativity

We use the entanglement negativity, a bipartite measure of entanglement in mixed quantum states, to study how multipartite entanglement constrains the real-space structure of the ground state wavefunctions of $(2+1)$-dimensional topological phases. We focus on the (Abelian) Laughlin and (non-Abelian) Moore-Read states at filling fraction $\nu=1/m$. We show that a combination of entanglement negativities, calculated with respect to specific cylinder and torus geometries, determines a necessary condition for when a topological state can be disentangled, i.e., factorized into a tensor product of states defined on cylinder subregions. This condition, which requires the ground state to lie in a definite topological sector, is sufficient for the Laughlin state. On the other hand, we find that a general Moore-Read ground state cannot be disentangled even when the disentangling condition holds.

Probing tripartite entanglement and coherence dynamics in pure and mixed independent classical environments

The type of environments to which a quantum system is exposed has a significant impact on the quantum system’s entanglement and coherence protection. In this regard, we investigate the time evolution of tripartite entanglement and coherence in GHZ-like state when subject to independent classical environments. In particular, we focus on local environments with the same and mixed disorders, resulting in various Gaussian noisy conditions, namely pure power-law noise, pure fractional Gaussian noise, power-law noise maximized, and fractional Gaussian noise maximized configurations. We show that the environments with mixed disorders are more detrimental than those having single kind of disorder for entanglement and coherence preservation using time-dependent quantum negativity, entanglement witnesses, purity, and decoherence metrics. Besides, there is no ultimate solution for avoiding the negative consequences of fractional Gaussian noise-assisted classical environments in both pure and mixed noise conditions. Not only the noise, but also the number of qubits driven by a certain noise, has been discovered to strongly influence the amount, nature of the decay, and preservation intervals. We also show that the GHZ-like states can be modelled in classical channels driven by pure power-law noise for extended quantum correlations, coherence, and quantum information preservation. In addition, we compare the entanglement measurement efficiency between entanglement witness and negativity measures.

Quantum speed limit and geometric measure of entanglement

Using the approach offered by quantum speed limit, we show that geometric measure of multipartite entanglement for pure states [Phys. Rev. A 68, 042307(2003)] can be interpreted as the minimal time necessary to unitarily evolve a given quantum state to a separable one.