Monotonicity of the quantum linear programming bound

  • Authors:

  • E. M. Rains

  • Affiliations:

  • Shannon Lab., AT&T Res., Florham Park, NJ

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 1999

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Abstract

The most powerful technique known at present for bounding the size of quantum codes of prescribed minimum distance is the quantum linear programming bound. Unlike the classical linear programming bound, it is not immediately obvious that if the quantum linear programming constraints are satisfiable for dimension K, then the constraints can be satisfied for all lower dimensions. We show that the quantum linear programming bound is monotonic in this sense, and give an explicitly monotonic reformulation