On the Existence of a Residue Entangled State in eLOCC Transformations

          @misc{ pirsa_PIRSA:11070065,
            doi = {10.48660/11070065},
            url = {https://pirsa.org/11070065},
            author = {Deviat, Monika},
            keywords = {},
            language = {en},
            title = {On the Existence of a Residue Entangled State in eLOCC Transformations},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {jul},
            note = {PIRSA:11070065 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum entanglement is a valuable resource in the field of quantum information science and allows one to accomplish many information processing tasks. In quantum transformations an entangled state A can be converted to another state B through local operations assisted by classical communication (LOCC). It has also been demonstrated that there exist entangled states A, B, C such that state A cannot be converted to a state B, but A otimes C can be converted to B otimes C by LOCC, where C is a suitably chosen entangled state acting as the catalyst. This is known as entanglement assisted LOCC or eLOCC. I will show that for certain A and B it is possible to obtain an extra entangled state R, called the residue entangled state in an eLOCC transformation. That is to say A otimes C can be converted to B otimes R otimes C even though A cannot be converted to B by LOCC. I will discuss the necessary and sufficient conditions for such a transformation to occur.