Complete monogamy of the multipartite quantum mutual information
arXiv:2211.07952 · doi:10.1103/PhysRevA.107.042409
Abstract
Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information (MQMI) based on the von Neumann entropy according to the framework of the complete measure of multi-particle quantum system. We show that these two MQMI are complete, monogamous on pure states, and one of them is not only completely monogamous but also tightly complete monogamous while another one is not. Moreover, we present another two MQMI by replacing the von Neumann entropy with the Tasllis -entropy from the former two ones. It is proved that one of them displays some degree of ``completeness'' as a measure of multi-particle quantum system, but the other one is not even non-negative and thus it can not be a alternative of MQMI. We also discuss the triangle relation for these three alternatives of MQMI. It is shown that the triangle inequalities hold for the former two MQMI as that of entanglement measure but the later one fails. By comparison, we found that the von Neumann entropy is better than other versions of entropy as desired when we characterize the quantum correlation in multi-particle system.
10 pages, one table. Some errors and typoes are corrected
References in corpus (18)
- Entanglement detection
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Quantum discord and the power of one qubit
- General Monogamy Inequality for Bipartite Qubit Entanglement
- On the quantum, classical and total amount of correlations in a quantum state
- Quantum information can be negative
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- Is Entanglement Monogamous?
- Experimental Quantum Teleportation of a Two-Qubit Composite System
- On polynomial invariants of several qubits
- Subadditivity of q-entropies for q>1
- Polynomial invariants for discrimination and classification of four-qubit entanglement
- Genuine multipartite entanglement measure
- Quantum correlation exists in any non-product state
- Monogamy of quantum discord
- Quantum correlation induced by the average distance between the reduced states
- When is a Genuine Multipartite Entanglement Measure Monogamous?