All multipartite Bell correlation inequalities for two dichotomic observables per site

We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit non-linear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.Comment: 11 pages, REVTe

Diffusion Tensor Imaging in a Large Longitudinal Series of Patients With Cervical Spondylotic Myelopathy Correlated With Long-Term Functional Outcome

BACKGROUND Fractional anisotropy (FA) of the high cervical cord correlates with upper limb function in acute cervical cord injury. We investigated the correlation between preoperative FA at the level of maximal compression and functional recovery in a group of patients after decompressive surgery for cervical spondylotic myelopathy (CSM). OBJECTIVE To determine the usefulness of FA as a biomarker for severity of CSM and as a prognostic biomarker for improvement after surgery. METHODS Patients received diffusion tensor imaging (DTI) scans preoperatively. FA values of the whole cord cross-section at the level of maximal compression and upper cervical cord (C1-2) were calculated. Functional status was measured using the modified Japanese Orthopedic Association (mJOA) scale preoperatively and at follow-up up to 2 yr. Regression analysis between FA and mJOA was performed. DTI at C4-7 was obtained in controls. RESULTS Forty-four CSM patients enrolled prior to decompression were compared with 24 controls. FA at the level of maximal compression correlated positively with preoperative mJOA score. Preoperative FA correlated inversely with recovery throughout the postoperative period. This was statistically significant at 12 mo postoperation and nearly so at 6 and 24 mo. Patients with preoperative FA0.55. CONCLUSION In the largest longitudinal study of this kind, FA promises a valid biomarker for severity of CSM and postoperative improvement. FA is an objective measure of function and could provide a basis for prognosis. FA is particularly useful if preoperative values are less than 0.55

Entanglement and communication-reducing properties of noisy N-qubit states

We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -- not requiring their further modification via stochastic local operations and classical communication such as entanglement purification or distillation procedures. We identify novel families of multi-particle states which are entangled but nevertheless allow local realistic description of specific Bell experiments. For some of them, the "gap" between the critical values for entanglement and violation of Bell inequality remains finite even in the limit of infinitely many qubits.Comment: new version, more results adde