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For instance, if N is even, $\\langle{\\hat{Z}_N(t^*)}\\rangle=\\langle{\\hat{Z}_1(0)}\\rangle$ , $\\langle{\\hat{X}_1\\hat{X}_N(t^*)}\\rangle=\\langle{\\hat{X}_1\\hat{X}_N(0)}\\rangle$ and $\\langle{\\hat{X}_1\\hat{Y}_N(t^*)}\\rangle=\\langle{\\hat{Y}_1\\hat{X}_N(0)}\\rangle$ . If qubit N has been projected onto \u2223\u2009\u00b1 N \u232a [for which $\\langle{\\hat{X}_N(0)}\\rangle=\\pm(-1)^{\\frac{N}{2}}$ ], we have $\\langle{\\hat{Z}_N(t^*)}\\rangle=\\langle{\\hat{Z}_1(0)}\\rangle$ , $\\langle{\\hat{X}_1\\hat{X}_N(t^*)}\\rangle=\\pm(-1)^{\\frac{N}{2}}\\langle{\\hat{X}_1(0)}\\rangle$ and $\\langle{\\hat{X}_1\\hat{Y}_N(t^*)}\\rangle=\\pm(-1)^{\\frac{N}{2}}\\langle{\\hat{Y}_1(0)}\\rangle$ . The state of spin N, after the measurement performed on spin 1, will satisfy $\\langle{\\hat{Z}_N(t^*)}\\rangle=\\langle{\\hat{Z}_1(0)}\\rangle$ , $\\langle{\\hat{X}_N(t^*)}\\rangle=(-1)^{\\frac{N}{2}}c\\,\\langle{\\hat{X}_1(0)}\\rangle$ and $\\langle{\\hat{Y}_N(t^*)}\\rangle=(-1)^{\\frac{N}{2}}c\\,\\langle{\\hat{Y}_1(0)}\\rangle$ , where c is the product of the measurement outcomes at 1 (after the evolution) and N (before the evolution). The state $(\\hat{Z}^{\\frac{N}{2}})\\rho^{in}(\\hat{Z}^{\\frac{N}{2}})$ [ $(\\hat{Z}^{\\frac{N}{2}+1})\\rho^{in}(\\hat{Z}^{\\frac{N}{2}+1})$ ] satisfies these conditions for c\u2009=\u20091 (c\u2009=\u2009\u2212\u20091)"},{"key":"14_CR11","doi-asserted-by":"publisher","first-page":"42316","DOI":"10.1103\/PhysRevA.76.042316","volume":"76","author":"C. Franco Di","year":"2007","unstructured":"Di Franco, C., et al.: Phys. Rev. A\u00a076, 042316 (2007)","journal-title":"Phys. Rev. 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