Deterministic Three-Copy Entanglement Concentration of Photons through Direct Sum Extension and Auxiliary Degrees of Freedom

The schematic optical realization of deterministic multicopy (three-copy) entanglement concentration under local operations and classical communication (LOCC) is presented, which can resort to the linear optical elements, controlled-NOT gate that uses weak cross-Kerr nonlinearity effect and entangled qudits with different degrees of freedom. This concentration is based on Nielsen's theorem, which in principle quantifies the unit success probability. In addition, the required positive operator-valued measurement (POVM) is implemented through direct sum extension, because the least number of ancillary dimensions is demanded. The construction of POVM is systematically formulated, which results in the feasibility to generate the protocol to n-copy (n>3) cases.