Computable and operationally meaningful multipartite entanglement measures

Abstract

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state, $|\psi ⟩$, for these applications is often directly related to the degree or type of entanglement present in $|\psi ⟩$. 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.

arXiv comment5+15 pages. 3+4 figures. Small errors in supplementary material corrected

References in corpus (41)

• Quantum entanglement
• Quantum Cryptography
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The Quantum Internet
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Satellite-to-ground quantum key distribution
• Quantum fingerprinting
• Conditions for a class of entanglement transformations
• Quantum teleportation using active feed-forward between two Canary Islands
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Global entanglement in multiparticle systems
• Longer-Baseline Telescopes Using Quantum Repeaters
• Substituting Quantum Entanglement for Communication
• Decoherence and multipartite entanglement
• Entanglement and the Power of One Qubit
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Distributed quantum sensing in a continuous variable entangled network
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Entanglement in Quantum Information Theory
• A potential multipartide entanglement measure
• Classification of multipartite entangled states by multidimensional determinants
• Learning the quantum algorithm for state overlap
• Monotones and invariants for multi-particle quantum states
• Quantum Algorithms: Entanglement Enhanced Information Processing
• Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
• Teleportation Systems Towards a Quantum Internet
• Genuine Network Multipartite Entanglement
• Multipartite entanglement detection in bosons
• Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom
• Truncated nonlinear interferometry for quantum enhanced atomic force microscopy
• Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems
• The controlled SWAP test for determining quantum entanglement
• Entanglement spectroscopy with a depth-two quantum circuit
• Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
• Critical sets of the total variance of state detect all SLOCC entanglement classes
• Bipartite entanglement in fermion systems
• One-body entanglement as a quantum resource in fermionic systems
• Quantum interactive proofs and the complexity of separability testing

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• Classical Splitting of Parametrized Quantum Circuits
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• Multipartite entanglement measures via Bell basis measurements
• A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
• Complete Genuine Multipartite Entanglement Monotone
• Geometric genuine multipartite entanglement for four-qubit systems
• Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states