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Local-operator entanglement (LOE) quantifies simulation complexity and reveals quantum magic resources. LOE is bounded by magic monotones, suggesting complex operator evolution implies inefficient classical simulation.

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Area of Science:

  • Quantum Information Theory
  • Many-Body Physics
  • Computational Complexity

Background:

  • Local-operator entanglement (LOE) is crucial for simulating quantum systems with tensor networks.
  • LOE is linked to many-body chaos in local quantum dynamics.

Purpose of the Study:

  • To investigate the relationship between LOE and the non-Clifford nature (magic resources) of unitary operations.
  • To establish bounds on LOE using magic monotones.

Main Methods:

  • Theoretical analysis of LOE and its relationship with magic monotones.
  • Proving upper bounds for LOE using T-count, unitary nullity, and operator-stabilizer Rényi entropy.
  • Analyzing average-case behavior for large, random quantum circuits.

Main Results:

  • LOE is upper-bounded by three distinct magic monotones: T-count, unitary nullity, and operator-stabilizer Rényi entropy.
  • For large random circuits, LOE and magic monotones approximately coincide on average.
  • Operator evolution that is hard to simulate with tensor networks is also hard for stabilizer and Pauli truncation methods.

Conclusions:

  • LOE serves as a unified measure of nonclassical resources in the operator space.
  • The findings imply that nonintegrable spin chains are classically intractable.
  • Quantum simulation complexity is intrinsically linked to the magic content of unitary operations.