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Quantum stabilizer formalism for any composite system

Zhelin Tian

Abstract

In this paper, we try to generalise quantum stabilizer formalism to any composite system, that is, it includes not only composite systems of equal dimensions, but also composite systems of unequal dimensions.

Quantum stabilizer formalism for any composite system

Abstract

In this paper, we try to generalise quantum stabilizer formalism to any composite system, that is, it includes not only composite systems of equal dimensions, but also composite systems of unequal dimensions.
Paper Structure (10 sections, 4 theorems, 39 equations, 1 figure)

This paper contains 10 sections, 4 theorems, 39 equations, 1 figure.

Table of Contents

  1. Definition of Qudit
  2. Extended Pauli operators and Weyl operators
  3. Global Pauli Group
  4. Definition of Stabilizer
  5. Trivial and Nontrivial stabilizer
  6. Generators and Independent Generators
  7. Definition of generator
  8. Independent generating set
  9. A Conjecture
  10. Acknowledgments

Key Result

Proposition 3.1

$G_{k_1\times k_2\cdots\times k_n}$ is well-defined.

Figures (1)

  • Figure 1: Pauli's Dream - The World ClockPaulidream

Theorems & Definitions (18)

  • Definition 1.1
  • Example 1.1
  • Definition 2.1
  • Definition 2.2
  • Definition 3.1
  • Proposition 3.1
  • proof
  • Example 3.1
  • Definition 4.1
  • Proposition 4.1
  • ...and 8 more