How entangled can a multi-party system possibly be?

Abstract

The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\dots ,d_n$, an upper bound for maximally allowable entanglement is derived in terms of geometric measure of entanglement. This upper bound is characterized exclusively by the dimensions $d_1,\dots ,d_n$ of composite subsystems. Numerous examples demonstrate that the upper bound appears to be reasonably tight.

arXiv comment11 pages, submitted for publications. Comments are welcome!

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• Hermitian Tensor Decompositions
• Quantum Higher Order Singular Value Decomposition
• Separability of Hermitian Tensors and PSD Decompositions