A new genuine tripartite entanglement measure is revealed, interpreted as the area of a so-called concurrence triangle. The new measure is found superior to previous attempts. Specific examples are illustrated.
Although genuine multipartite entanglement has already been generated and verified by experiments, most of the existing measures cannot detect genuine entanglement faithfully. In this work, by exploiting for the first time a previously overlooked constraint for the distribution of entanglement in three-qubit systems, we reveal a new genuine tripartite entanglement measure, which is related to the area of a so-called concurrence triangle. It is compared with other existing measures and is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space. The properties of the triangle measure make it a candidate in potential quantum tasks and available to be used in any multiparty entanglement problems.
Genuine multipartite entanglement is crucial for quantum information and quantum technologies but quantifying it has been a long-standing challenge. Most existing measures do not meet a “genuine” requirement, making them unsuitable for many applications. Here, we present a surprising triangle measure for tripartite entanglement, and introduce the extension to four-qubit systems. We discuss potential avenues for further generalizations along this geometric path. This indicates that our work may pave the way for further advancements.
Quantifying genuine entanglement is a crucial task in quantum information
theory. Very recently, a genuine three-qubit entanglement measure induced by
the area of concurrence triangle was proposed in [Phys. Rev. Lett., 127,
040403]. In this work, we show that this scenario is also valid for any other
entanglement measure and system with any dimension. Moreover, in light of the
triangle structure, we give genuine entanglement measures for any four-partite
system via the complete tripartie entanglement measure and the triangle measure
respectively.
Abstract Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, we give an approach of constituting genuine m -partite entanglement measures from any bipartite entanglement and any k -partite entanglement measure, 3 ⩽ k < m . In addition, as a complement to the three-qubit concurrence triangle proposed in ( Phys. Rev. Lett. 127 040403), we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.