Multipartite Entanglement Research Articles

Entanglement Detection: A Scoping Review

Quantum entanglement is a critical physical process in quantum mechanics and quantum information theory. It is a required process in quantum computing, quantum teleportation, and quantum cryptography. Entanglement detection affects the performance of quantum information processing tasks. Entanglement detection has grown in popularity over the years, and various entanglement detection methods are available, though some have application and system scale limitations. This scoping review sought to identify various measurement methods for entanglement detection in both bipartite and multipartite entanglement systems. Secondary resource indexed literatures were selected based on specific keywords from literatures published between 2017 and 2021. The goal of this study is to present a proposed conceptual framework of entanglement detection based on previous work as a guidance and reference founded on one’s specific requirements.

Certification of genuine multipartite entanglement in spin ensembles with measurements of total angular momentum

Certification of genuine multipartite entanglement in spin ensembles with measurements of total angular momentum

Multipartite entanglement detection via generalized Wigner–Yanase skew information

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate k-nonseparability and k-partite entanglement of N-partite quantum systems from the perspective of the generalized Wigner–Yanase skew information. We deduce the upper bounds on the generalized Wigner–Yanase skew information of k-separable states and k-producible states in arbitrary dimensional multipartite quantum systems. And based on the upper bounds, we develop two different approaches in form of simple inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner–Yanase skew information. Any violation of these inequalities by a quantum state reveals its k-nonseparability or k-partite entanglement, so these inequalities present the hierarchic classifications of k-nonseparability or k-partite entanglement for all N-partite quantum states from N-nonseparability to 2-nonseparability or from 2-partite entanglement to N-partite entanglement. Some well-known entanglement criteria are the special cases of our criteria. We illustrate the significance of our criteria by showing that they can reveal k-nonseparability and k-partite entanglement undetectable by well-known criteria through several typical examples, and their advantages over well-known criteria.

The controlled SWAP test for entanglement of mixed quantum states

Quantum entanglement plays a key role in the field of quantum computing and quantum communication. The controlled SWAP test has been used to detect pure state entanglement (Foulds S. et al. Quantum Sci. Technol., 6 (2021) 035002; Beckey J. L. et al. Phys. Rev. Lett., 127 (2021) 140501). In this paper, we investigate that quantum circuits for controlled SWAP test can be used to detect the entanglement of multipartite mixed state. Based on the measured probability, we propose entanglement criteria for detecting multipartite entanglement and genuine entanglement of pure states. In addition, we give representation of the entanglement measures based on the measured probability of the controlled SWAP tests. Numerical examples are used to illustrate the efficiency of the entanglement criteria.

Demonstration of hypergraph-state quantum information processing

Complex entangled states are the key resources for measurement-based quantum computations, which is realised by performing a sequence of measurements on initially entangled qubits. Executable quantum algorithms in the graph-state quantum computing model are determined by the entanglement structure and the connectivity of entangled qubits. By generalisation from graph-type entanglement in which only the nearest qubits interact to a new type of hypergraph entanglement in which any subset of qubits can be arbitrarily entangled via hyperedges, hypergraph states represent more general resource states that allow arbitrary quantum computation with Pauli universality. Here we report experimental preparation, certification and processing of complete categories of four-qubit hypergraph states under the principle of local unitary equivalence, on a fully reprogrammable silicon-photonic quantum chip. Genuine multipartite entanglement for hypergraph states is certificated by the characterisation of entanglement witness, and the observation of violations of Mermin inequalities without any closure of distance or detection loopholes. A basic measurement-based protocol and an efficient resource state verification by color-encoding stabilizers are implemented with local Pauli measurement to benchmark the building blocks for hypergraph-state quantum computation. Our work prototypes hypergraph entanglement as a general resource for quantum information processing.

Eigenvalue-based quantum state verification of three-qubit W class states

In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.

Extracting many-body quantum resources within one-body reduced density matrix functional theory

Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation, detect quantum phase transitions, witness genuine multipartite entanglement, or probe nonlocality. Despite this widespread range of applications, computing the QFI value of quantum many-body systems is, in general, a very demanding task. Here we combine ideas from functional theories and quantum information to develop a functional framework for the QFI of fermionic and bosonic ground states. By relying upon the constrained-search approach, we demonstrate that the QFI matrix terms can universally be determined by the one-body reduced density matrix (1-RDM), thus avoiding the use of exponentially large wave functions. Furthermore, we show that QFI functionals can be determined from the universal 1-RDM functional by calculating its derivatives with respect to the coupling strengths, thus becoming the generating functional of the QFI. We showcase our approach with the Bose-Hubbard model and present exact analytical and numerical QFI functionals. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information. Published by the American Physical Society 2024

Petz recovery from subsystems in conformal field theory

We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals A, B and C on a spatial slice, where we can view these quantities as measuring correlations between A and C that are not mediated by the region B that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where A and C are close using the OPE expansion. In the case where A and C are far apart, we find a surprising non-commutativity of the replica trick with the OPE limit. For all values of the cross-ratio, the fidelity is strictly better than a general information-theoretic lower bound in terms of the conditional mutual information. We also compare the mutual information between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.

Experimental distillation of tripartite quantum steering with an optimal local filtering operation

Multipartite Einstein-Podolsky-Rosen (EPR) steering admits multipartite entanglement in the presence of uncharacterized verifiers, enabling practical applications in semi-device-independent protocols. Such applications generally require stronger steerability, while the unavoidable noise weakens steerability and consequently degrades the performance of quantum information processing. Here, we propose the local filtering operation that can maximally distill genuine tripartite EPR steering from N copies of three-qubit generalized Greenberger-Horne-Zeilinger states, in the context of two semi-device-independent scenarios. The optimal filtering operation is determined by the maximization of assemblage fidelity. Analytical and numerical results indicate the advantage of the proposed filtering operation when N is finite and the steerability of initial assemblages is weak. Experimentally, a proof-of-principle demonstration of two-copy distillation is realized with the optical system. The advantage of the optimal local filtering operation is confirmed by the distilled assemblage in terms of higher assemblage fidelity with perfectly genuine tripartite steerable assemblages, as well as the greater violation of the inequality to witness genuine tripartite steerable assemblages. Our results benefit the distillation of multipartite EPR steering in practice, where the number of copies of initial assemblages is generally finite.

Multipartite Entanglement: A Journey through Geometry.

Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the "genuine" requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems.

Photonic Which-Path Entangler Based on Longitudinal Cavity-Qubit Coupling.

We show that a modulated longitudinal cavity-qubit coupling can be used to control the path taken by a multiphoton coherent-state wave packet conditioned on the state of a qubit, resulting in a qubit-which-path (QWP) entangled state. QWP states can generate long-range multipartite entanglement using strategies for interfacing discrete- and continuous-variable degrees of freedom. Using the approach presented here, entanglement can be distributed in a quantum network without the need for single-photon sources or detectors.

Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems.

Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.

Pseudo entropy under joining local quenches

We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs.

Steady motional entanglement between two distant levitated nanoparticles

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Monotonicity conjecture for multi-party entanglement. Part I

In this paper, we conjecture a monotonicity property that we call monotonicity under coarse-graining for a class of multi-partite entanglement measures. We check these properties by computing the measures for various types of states using different methods.

Multipartite entanglement serves as a faithful detector for quantum phase transitions

We investigate quantum phase transitions (QPTs) in various spin chain systems using the multipartite entanglement measure τSEF based on the monogamy inequality of squared entanglement of formation (EOF). Our results demonstrate that τSEF is more effective and reliable than bipartite entanglement or bipartite correlation measures such as EOF, von Neumann entropy, and quantum discord in characterizing QPTs. τSEF not only detects critical points that may go unnoticed by other detectors but also avoids the issue of singularity at non-critical points encountered by other measures. Furthermore, by applying τSEF , we have obtained the phase diagram for the XY spin chain with three and four interactions and discovered a new quantum phase.

Activation of metrologically useful genuine multipartite entanglement

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state is weakly entangled and not even more useful than separable states. This way we activate metrologically useful genuine multipartite entanglement. Remarkably, not only that the maximally achievable metrological usefulness is attained exponentially fast in the number of copies, but it can be achieved by the measurement of few simple correlation observables. We also make general statements about the usefulness of a single copy of pure entangled states. We surprisingly find that the multiqubit states presented in Hyllus et al (2010 Phys. Rev. A 82 012337), which are not useful, become useful if we embed the qubits locally in qutrits. We discuss the relation of our scheme to error correction, and its possible use for quantum metrology in a noisy environment.

Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA.

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a well-known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the αth-power (α≥4ln2) of LCREN, and polygamy inequalities utilizing the αth-power (0≤α≤2) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high-dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions.

Detection and measure of genuine entanglement based on the realignment of density matrices for tripartite quantum states

As one of the important types of entanglement, genuine multipartite entanglement plays a key role in both foundational and practical aspects of quantum information theory. In this manuscript, we study the genuine multipartite entanglement in tripartite quantum systems based on the enhanced realignment criterion. A family of sufficient conditions for detecting genuine tripartite entanglement are presented. Moreover, lower bounds of the genuine multipartite entanglement concurrence are derived. The detection power and advantages of our results are illustrated through several examples.

Measurement-induced multipartite-entanglement regimes in collective spin systems

We study the competing effects of collective generalized measurements and interaction-induced scrambling in the dynamics of an ensemble of spin-1/2 particles at the level of quantum trajectories. This setup can be considered as analogous to the one leading to measurement-induced transitions in quantum circuits. We show that the interplay between collective unitary dynamics and measurements leads to three regimes of the average Quantum Fisher Information (QFI), which is a witness of multipartite entanglement, as a function of the monitoring strength. While both weak and strong measurements lead to extensive QFI density (i.e., individual quantum trajectories yield states displaying Heisenberg scaling), an intermediate regime of classical-like states emerges for all system sizes where the measurement effectively competes with the scrambling dynamics and precludes the development of quantum correlations, leading to sub-Heisenberg-limited states. We characterize these regimes and the crossovers between them using numerical and analytical tools, and discuss the connections between our findings, entanglement phases in monitored many-body systems, and the quantum-to-classical transition.