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No-Go Theorems for Quantum Resource Purification.

Kun Fang1,2, Zi-Wen Liu3

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom.

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|August 27, 2020
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Summary
This summary is machine-generated.

Quantum mechanics fundamentally limits the purification of noisy quantum resources, proving perfect purification is impossible even probabilistically. This impacts quantum information science applications and fault-tolerant quantum computation.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation

Background:

  • Quantum resources like entanglement and coherence are vital for quantum technologies.
  • Noise contaminates these resources, necessitating purification for reliable use.
  • Resource purification is crucial for unlocking quantum advantages over classical methods.

Purpose of the Study:

  • To establish fundamental, universally applicable limitations on the purification of noisy quantum resources.
  • To derive nontrivial lower bounds on the error in converting noisy states to pure resource states.
  • To analyze the implications of these limitations for quantum resource distillation and fault-tolerant quantum computation.

Main Methods:

  • Theoretical derivation of fundamental limitations using quantum mechanics.
  • Establishing nontrivial lower bounds on the error of purification protocols.
  • Analyzing the impact on generic noisy states and resource conversion.

Main Results:

  • Proved that perfect purification of generic noisy quantum resources is impossible, even probabilistically.
  • Derived general lower bounds on the error of any purification protocol.
  • Demonstrated strong limits on the efficiency of quantum resource distillation.

Conclusions:

  • The laws of quantum mechanics impose inherent limits on resource purification efficiency.
  • These findings have significant implications for the resource cost of magic state distillation.
  • The results inform the development of more efficient quantum error correction and fault-tolerant architectures.