Locally undetermined states, generalized schmidt decomposition, and application in deistributed comuting

  • Authors:

  • Yuan Feng;Runyao Duan;Mingsheng Ying

  • Affiliations:

  • State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China and University of Technology, Sydney, Australia;State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China and University of Technology, Sydney, Australia;State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China and University of Technology, Sydney, Australia

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2009

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Abstract

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit 'high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.