Genuine multipartite entanglement measures based on multi-party teleportation capability

Abstract

Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for $N$-qubit systems, where $N\ge 4$, and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.

arXiv comment14 pages, 2 figures

References in corpus (25)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Three qubits can be entangled in two inequivalent ways
• Quantum secret sharing
• Quantum-enhanced measurements: beating the standard quantum limit
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Entanglement detection
• Measurement-based quantum computation
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Teleportation and Dense Coding with Genuine Multipartite Entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• Teleportation, Bell's Inequalities and Inseparability
• Quantum teleportation via a W state
• Local environment can enhance fidelity of quantum teleportation
• Multipartite Entanglement Signature of Quantum Phase Transitions
• A Triangle Governs Genuine Tripartite Entanglement
• Genuine Multipartite Entanglement in Quantum Phase Transitions
• Multipartite entanglement in quantum spin chains
• Optimal distillation of a GHZ state
• Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Entanglement of three-qubit pure states in terms of teleportation capability
• Tripartite entanglement measure under local operations and classical communication
• Conference Key Agreement and Quantum Sharing of Classical Secrets with Noisy GHZ States

Cited by in corpus (5)

• Multipartite entanglement measures: a review
• Investigating controlled teleportation capability of quantum states with respect to $k$-separability
• A Sharp Geometric Measure of Entanglement
• Entanglement of Assistance as a measure of multiparty entanglement
• Entanglement dynamics in minimal Kitaev chains