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Extra info for Classical mechanics, quantum mechanics, field theory
K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 78(10), 2031 (1997) 20. H. P. A. K. Wootters, Mixed-state entanglement and quantum error correction. Phys. Rev. A 54(5), 3824–3851 (1996) 30 2 Exploiting Quench Dynamics in Spin Chains 21. J. A. Nielsen, Entanglement in a simple quantum phase transition. Phys. Rev. A 66(3), 032110 (2002) 22. -P. Breuer, F. Petruccione, The theory of open quantum systems. (Clarendon Press, Oxford, UK, 2002) 23.
In general, convenient to express q ^ on the state space of the chain composed of N spin-1=2 particles any operator A may be decomposed into ^¼ A 22N X h i ^k ^ ky X ^X Tr q ð2:10Þ k¼1 h i À Á ^k ; X ^ l Tr X ^ l ¼ dk;l ^ yX X k ð2:11Þ 20 2 Exploiting Quench Dynamics in Spin Chains X ^k ¼ 1 X ð2:12Þ k which is sometimes referred to as Hilbert–Schmidt operator decomposition . For an operator A defined on the Hilbert space spanned by the two spin-12 degrees of freedom associated to site l of a spin chain configuration it is convenient to choose the following set of orthogonal operators: n o ^ ¼ r ^" ^# ^þ ^À l ¼ 1; 2; .
However, our data for Tmax in a quench N suggesting that the process of D : 1 ! 0 are seen to obey the scaling Tmax $ pJ establishing entanglement is slightly slower than this estimate. Yet, the linear scaling with N is otherwise consistent with the causal cone picture. This delay hints towards a collective effect, leading to an optimal entanglement as a result of many such local events. The excitation that is emitted from the centre of the chain (meaningful in the case of odd N) will, at the optimal time Tmax , have encountered the terminal sites and will have been reflected from the boundaries.