Entanglement criterion

In the case of the perfect symmetry between subharmonic modes (71 = 72 = 7, 1 = 62 = S) this criterion is reduced to the following form V = I7 IA < I. while for the product of variances this criterion has the form V+ V- = V2 < 1. The strong CV entanglement criterion shows that when the inequality... 

In order to deduce whether we fulfil the entanglement criterion (18) we compare the above to our expectation from Eq. (16a). For the verifying pulse we get... 

Using these relations we rewrite the variance sum in the entanglement criterion as... 

If S(a)<0, corresponding to correlation Fuia) is lower than the quantum limit 2, it follows that the tripartite entanglement criterion is satisfied. 

Any system of chains with N < Nc will not satisfy the entanglement criterion. In other words, for a system with N < Net ny sphere drawn around the entire chain with diameter De = < (p > ) will contain... 

Fig. 4 Definition of the tube diameter, a, also called L a (length a) and the entanglement criterion of n. Image adapted with permission from Ref. [26], copyright of the original version, 2005 Elsevier...

The entanglement criterion for necklaces is similar to that for a normal PE. Also, the number of entanglement sites is the same, and the entanglement concentration can be determined by Ce = n c [94]. The only difference is the tube diameter and the correlation length defining it. The relaxation time, self-diffusion coefficient and viscosity of entangled PE necklaces can be determined by [94] ... 

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