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arXiv:quant-ph/0609027 · Physical Review A

Information-theoretic measure of genuine multiqubit entanglement

Jianming Cai, Zheng-Wei Zhou, Xingxiang Zhou, Guang‐Can Guo

Published Oct 27, 2006• 23 citations
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Abstract

We consider pure quantum states of $N$ qubits and study the genuine $N$-qubit entanglement that is shared among all the $N$ qubits. We introduce an information-theoretic measure of genuine $N$-qubit entanglement based on bipartite partitions. When $N$ is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When $N$ is an odd number, the measure can also be obtained in principle.

DOI
10.1103/physreva.74.042338

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Although quantum entanglement has already been verified experimentally and applied in quantum computing, quantum sensing and quantum networks, most of the existing measures cannot characterize the entanglement faithfully. In this work, by exploiting the Schmidt decomposition of a bipartite state ∣ψ⟩AB|ψ\rangle_{AB}∣ψ⟩AB​, we first establish a one-to-one correspondence relation between the characteristic polynomial of the reduced state ρAρ_AρA​ and the polynomials its trace. Then we introduce a family of entanglement measures which are given by the complete eigenvalues of the reduced density matrices of the system. Specific measures called informationally complete entanglement measures (ICEMs) are presented to illustrate the advantages. It is demonstrated that such ICEMs can characterize finer and distinguish better the entanglement than existing well-known entanglement measures. They also give rise to criteria of state transformations under local operation and classical communication. Moreover, we show that the ICEMs can be efficiently estimated on a quantum computer. The fully separability, entanglement and genuine multipartite entanglement can detected faithfully on quantum devices.