Recently it has been observed that the group
E7 can be used to describe a special type of quantum entanglement of seven qubits partitioned into seven tripartite systems. Here we show that this curious type of entanglement is entirely encoded into the discrete geometry of the Fano plane. We explicitly work out the details concerning a qubit interpretation of the
E7 generators as representatives of tripartite protocols acting on the 56-dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in four-dimensional string theory. We point out that there is a dual relationship between entangled subsystems containing three and four tripartite systems. This relationship is reflected in the structure of the expressions for the black hole entropy in the
N=4 and
N=2 truncations of the
E7(7) symmetric area form of
N=8 supergravity. We conjecture that a similar picture based on other qubit systems might hold for black hole solutions in magic supergravities.
A four-mode Gaussian state has two types of bipartitions: 1-3 partitions and 2-2 partitions. A 1-3 partition means that a single mode forms one subsystem and the remaining three modes form the other subsystem; A 2-2 partition means that two modes form one subsystem and the remaining two modes form the other subsystem. In this paper, we investigate the entanglement property of a four-mode bound entangled Gaussian state for different bipartitions via a linear matrix inequality method. The Gaussian state example under consideration was proposed by R. F. Werner and M. M. Wolf in [1]. The results could be helpfu for deepening our understanding of Gaussian entanglement.
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.