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理论物理通讯：英文版

A Criterion to Identify Maximally Entangled Four-Qubit State

查新未, 宋海洋, 冯峰

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Paolo Facchi,et al.[Phys.Rev.A 77 (2008)060304(R)]presented a maximally multipartite entangledstate (MMES).Here,we give a criterion for the identification of maximally entangled four-qubit states.Using thiscriterion,we not only identify some existing maximally entangled four-qubit states in the literature,but also find severalnew maximally entangled four-qubit states as well.

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Paolo Facchi,et al.[Phys.Rev.A 77 (2008)060304(R)]presented a maximally multipartite entangledstate (MMES).Here,we give a criterion for the identification of maximally entangled four-qubit states.Using thiscriterion,we not only identify some existing maximally entangled four-qubit states in the literature,but also find severalnew maximally entangled four-qubit states as well.
We first present a generalized criterion for maximally entangled states of 2–8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine eight-qubit maximally entangled state is obtained. For the four-, seven- and eight-qubit system in which no perfect maximally multi-qubit entangled state (MMES) was thought to exist before, we find that the proven four- and eight-qubit MMESs and the suspected seven-qubit MMES, are not completely mixed in subsystems with two, four and three qubits, respectively, but are completely mixed in subsystems with fewer qubits. The new criterion and MMES can play important roles in quantum information technology, such as teleportation and dense coding.
Recently, Paolo Facchi et al. [Phys. Rev. A. 77, 060304 (R) (2008)] introduced the notion of maximally multipartite entangled states of n qubits. Here, we give a criterion for faithful controlled teleportation of an arbitrary two-qubit state via a five-qubit entangled state and obtain the general relation between the genuine five-qubit entangled state and controlled teleportation. This criterion can be extended to teleportation of an arbitrary N-qubit state using 2N+1-qubit entangled state. Furthermore, we study the optimal match of measuring basis and quantum channel.
Abstract We present a generalized criterion for maximally entangled nine-qubit states, whose minimum averaged subsystem purity should be equal to 1/14. In this note, we prove that the absolutely maximally entangled state for nine qubits does not exist. In other words, we pronounce that the pure (9, 1, 5) 2 quantum error-correcting code does not exist. Further, we construct a new genuine nine-qubit maximally entangled states of 110,15 and 1 balanced purities equal to 1/16, 1/8 and 1/4, respectively. We found that the marginal density matrices for subsystems of 1,2,3- qubits all completely mixed in these states; therefore, maximally entangled nine-qubit state is a 3-uniform state.