Noiseless method for checking the Peres separability criterion by local operations and classical communication

We present a method for checking the Peres separability criterion in an arbitrary bipartite quantum state rho(AB) within local operations and classical communication scenario. The method does not require noise operation which is needed in making the partial transposition map physically implementable. The main task for the two observers, Alice and Bob, is to measure some specific functions of the partial transposed matrix. With these functions, they can determine the eigenvalues of rho(T)(AB)(B), among which the minimum serves as an entanglement witness.

practical type checking of functions defined on context-free languages

A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF.languages is not decidable,a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked.Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.