Multipartite entanglement is one of the hallmarks of quantum mechanics and is central to quantum information processing. In this work we show that concentratable entanglement (CE), an operationally motivated entanglement measure, induces a hierarchy upon pure states from which different entanglement structures can be experimentally certified. In particular, we find that nearly all genuine multipartite entangled states can be verified through the CE. Interestingly, GHZ states prove to be far from maximally entangled according to this measure. Instead we find the exact maximal value and corresponding states for up to 18 qubits and show that these correspond to extremal quantum error correcting codes. The latter allows us to unravel a deep connection between CE and coding theory. Finally, our results also offer an alternative proof, on up to 31 qubits, that absolutely maximally entangled states do not exist. Published by the American Physical Society 2024
Multipartite entanglement is one of the hallmarks of quantum mechanics and is central to quantum information processing. In this work we show that concentratable entanglement (CE), an operationally motivated entanglement measure, induces a hierarchy upon pure states from which different entanglement structures can be experimentally certified. In particular, we find that nearly all genuine multipartite entangled states can be verified through the CE. Interestingly, GHZ states prove to be far from maximally entangled according to this measure. Instead we find the exact maximal value and corresponding states for up to 18 qubits and show that these correspond to extremal quantum error correcting codes. The latter allows us to unravel a deep connection between CE and coding theory. Finally, our results also offer an alternative proof, on up to 31 qubits, that absolutely maximally entangled states do not exist. Published by the American Physical Society 2024
The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds et al . 2021 Quantum Sci. Technol . 6 , 035002 (doi: 10.1088/2058-9565/abe458 )). We extend this, and the related measure concentratable entanglement (CE), to enable important practical applications in quantum information processing. We investigate the lower bound of concentratable entanglement given in (Beckey et al . 2023 Phys. Rev. A 107 , 062425 (doi: 10.1103/physreva.107.062425 )) and conjecture an upper bound of the mixed-state concentratable entanglement that is robust to c-SWAP test errors. Since experimental states are always slightly mixed, our work makes the c-SWAP test and CE measure suitable for application in experiments to characterize entanglement. We further present the CE of some key higher-dimensional states such as qudit states and entangled optical states to validate the CE as a higher-dimensional measure of entanglement. This article is part of the theme issue ‘The quantum theory of light’.
Multipartite entanglement is a fundamental aspect of quantum mechanics, crucial to advancements in quantum information processing and quantum computation. Within this field, Genuinely Multipartite Entanglement (GME), being entangled in all bipartitions, and Absolutely Maximally Entanglement (AME), maximally entangled in all bipartitions, represent two significant types of entanglement with diverse applications. In this work, we introduce a new measure called the GME-AME multipartite entanglement measure, with a non-zero value representing the GME states and the maximum value is reached only by the AME states. The measure is applied to study the multipartite entanglement of four partite systems using the operator to state mapping, and the four partite permutation qutrit states are classified according to the measure. With various examples, we show that our measure is robust in classifying the four partite entangled states.
Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Concentratable entanglement (CE), introduced recently, can be estimated from just two copies of a quantum state. Here, we propose generalized concentratable entanglement (GCE), a broader class of multipartite entanglement measures naturally tied to quantum Tsallis entropies, and present a parallelized protocol for estimating GCE across multiple state copies. Increasing the number of copies yields an improved error bound in the presence of imperfections. We prove that GCE is a well-defined entanglement monotone and conjecture some new entropic inequalities. Moreover, we demonstrate the concentration of entanglement into W states using three-state copies. Our results contribute to more robust and versatile characterizations of multipartite entanglement.
Multipartite entanglement is regarded as a crucial physical resource in quantum network communication. However, due to the intrinsic complexity of quantum many-body systems, identifying a multipartite entanglement measure that is both efficiently computable and capable of accurately characterizing entanglement remains a challenging problem. To address these issues, we propose a family of two-parameter multipartite entanglement measures for mixed states, termed unified-entropy concentratable entanglements. Many well-known multipartite entanglement measures are recovered as special cases of this family of measures, such as the entanglement of formation and the concentratable entanglements introduced in [Phys. Rev. Lett. 127, 140501 (2021)]. We demonstrate that the unified-entropy concentratable entanglements constitutes a well-defined entanglement monotones, and establish several desirable properties it satisfies, such as subadditivity and continuity. We further investigate the ordering relations of unified-entropy concentratable entanglements and discuss how these quantities can be efficiently estimated on near-term quantum devices. As an application, we demonstrate that the unified-entropy concentratable entanglements can effectively distinguish between multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and W states. The ordering relations of these entanglement measures are further validated using four-partite star quantum network states and four-qubit Dicke states. Moreover, we find that the unified-entropy concentratable entanglements exhibit greater sensitivity than the original concentratable entanglements in detecting certain four-partite star quantum network states.
Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Concentratable entanglement (CE), introduced recently, can be estimated from just two copies of a quantum state. Here, we propose generalized concentratable entanglement (GCE), a broader class of multipartite entanglement measures naturally tied to quantum Tsallis entropies, and present a parallelized protocol for estimating GCE across multiple state copies. Increasing the number of copies yields an improved error bound in the presence of imperfections. We prove that GCE is a well-defined entanglement monotone and conjecture some new entropic inequalities. Moreover, we demonstrate the concentration of entanglement into W states using three-state copies. Our results contribute to more robust and versatile characterizations of multipartite entanglement.
At the heart of the curious phenomenon of quantum entanglement lies the relation between the whole and its parts. In my thesis, I explore different aspects of this theme in the multipartite setting by drawing connections to concepts from statistics, graph theory, and quantum error-correcting codes: first, I address the case when joint quantum states are determined by their few-body parts and by Jaynes’ maximum entropy principle. This can be seen as an extension of the notion of entanglement, with less complex states already being determined by their few-body marginals. Second, I address the conditions for certain highly entangled multipartite states to exist. In particular, I present the solution of a long-standing open problem concerning the existence of an absolutely maximally entangled state on seven qubits. This sheds light on the algebraic properties of pure quantum states, and on the conditions that constrain the sharing of entanglement amongst multiple particles. Third, I investigate Ulam’s graph reconstruction problems in the quantum setting, and obtain legitimacy conditions of a set of states to be the reductions of a joint graph state. Lastly, I apply and extend the weight enumerator machinery from quantum error correction to investigate the existence of codes and highly entangled states in higher dimensions. This clarifies the physical interpretation of the weight enumerators and of the quantum MacWilliams identity, leading to novel applications in multipartite entanglement.