Invertible condition of quantum Fisher information matrix for a mixed qubit

Estimating multiparamter simultaneously as precise as possible is an important goal of quantum metrolo- gy. As a first step to this end, here we give a condition determining whether two arbitrary parameters can be estimated simultaneously for a qubit in the mixed state. An application of this condition is shown.Comment: The European Physical Journal D 201

Background field method in the large NfN_f expansion of scalar QED

Using the background field method, we, in the large $N_f$ approximation, calculate the beta function of scalar quantum electrodynamics at the first nontrivial order in $1/N_f$ by two different ways. In the first way, we get the result by summing all the graphs contributing directly. In the second way, we begin with the Borel transform of the related two point Green's function. The main results are that the beta function is fully determined by a simple function and can be expressed as an analytic expression with a finite radius of convergence, and the scheme-dependent renormalized Borel transform of the two point Green's function suffers from renormalons.Comment: 13 pages, 4 figures, 1 table, to appear in the European Physical Journal

The Relationship between Purchase Money Security Interest and Title Retention

The introduction of Purchase Money Security Interest (PMSI) to our country has expanded China's system of security interests. The structures of title retention and financial lease created based on parties' consensus are blurred by the function of security, deviating from the legal property rights, ignoring the true legal meaning of parties, and resulting in the effectiveness equivalent to security interests. Although title retention, financial leasing and PMSI all have the functional value of guaranteeing price claims, and Article 388 of the Civil Code has enriched the content of guarantee contracts by introducing the registration opposition rule into atypical guarantees, we should still adhere to the system logic of the dichotomy between property and debt in the Civil Code, and draw a clear line between the two under the principle of legal property rights. The influence of guarantee functionalism should be limited to expanding the scope of "other contracts with guarantee functions" in Article 388 of the Civil Code. The retention of ownership and financial lease in Article 57 of the Judicial Interpretation on the Guarantee System are actually linked to PMSI after being attached with various conditions, which is fundamentally different from the original system structure of Articles 641 and 735 of the Civil Code