Adding entanglement to quantum error-correcting codes

          @misc{ pirsa_PIRSA:10040029,
            doi = {10.48660/10040029},
            url = {https://pirsa.org/10040029},
            author = {Brun, Todd},
            keywords = {Quantum Information},
            language = {en},
            title = {Adding entanglement to quantum error-correcting codes},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {apr},
            note = {PIRSA:10040029 see, \url{https://pirsa.org}}
          }
          

Abstract

Shared entanglement between sender and receiver can enable more errors to be corrected than with a standard quantum error-correcting code. This extra error correction can be used either to boost the rate of the code--commonly seen in quantum codes constructed from classical linear codes--or to increase the error-correcting power of the code (as represented by, for example, the code distance). We will see how adding extra entanglement to a given quantum code can increase its distance, and discuss the optimization problem in maximizing the effectiveness of a given amount of added entanglement. We will also briefly examine some applications of entanglement-assistance to particular types of codes, such as LDPC codes and convolutional codes.