Devi A R Usha, Prabhu R, Rajagopal A K
Department of Physics, Bangalore University, Bangalore-560 056, India.
Phys Rev Lett. 2007 Feb 9;98(6):060501. doi: 10.1103/PhysRevLett.98.060501. Epub 2007 Feb 5.
We show that higher order intergroup covariances involving even number of qubits are necessarily positive semidefinite for N-qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order intergroup covariance matrices (2k</=N) of symmetric N-qubit systems. These conditions have a simple structure and detect entanglement in all even partitions of the symmetric multiqubit system. The observables involved are feasible experimental quantities and do not demand full state determination through quantum state tomography.
我们表明，对于在量子比特置换下完全对称的N量子比特可分态，涉及偶数个量子比特的高阶组间协方差必然是半正定的。这种识别基于对称N量子比特系统的2k阶组间协方差矩阵（2k≤N）的负性，导致了一族不可分离性的充分条件。这些条件具有简单的结构，并且能检测对称多量子比特系统所有偶划分中的纠缠。所涉及的可观测量是可行的实验量，不需要通过量子态层析成像来完全确定量子态。
