A surprisingly simple way of reversing trace distance via entanglement

  • Authors:

  • Jun Yan

  • Affiliations:

  • School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China,State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sc ...

  • Venue:
  • TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
  • Year:
  • 2012

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Abstract

Trace distance (between two quantum states) can be viewed as quantum generalization of statistical difference (between two probability distributions). On input a pair of quantum states (represented by quantum circuits), how to construct another pair, such that their trace distance is large (resp. small) if the original trace distance is small (resp. large)? That is, how to reverse trace distance? This problem originally arose in the study of statistical zero-knowledge quantum interactive proof. We discover a surprisingly simple way to do this job. In particular, our construction has two interesting features: first, entanglement plays a key role underlying our construction; second, strictly speaking, our construction is non-black-box.