Multi-level, multi-party singlets as ground states and their role in entanglement distribution

          @misc{ pirsa_PIRSA:07030013,
            doi = {10.48660/07030013},
            url = {https://pirsa.org/07030013},
            author = {Hadley, Christopher},
            keywords = {Quantum Information},
            language = {en},
            title = {Multi-level, multi-party singlets as ground states and their role in entanglement distribution},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {mar},
            note = {PIRSA:07030013 see, \url{https://pirsa.org}}
          }
          

Abstract

We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state. One implication of this is that the entanglement in these states is very robust (persistent), while an application is in establishing an arbitrary amount of entanglement between well-separated parties (for subsequent use as a communication resource) by local measurements on an appropriate graph. Based on quant-ph/0602139.