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Entanglement concentration is irreversible.

Wataru Kumagai1, Masahito Hayashi

  • 1Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan and Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan.

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|October 15, 2013
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Summary
This summary is machine-generated.

Entanglement concentration for quantum information is not perfectly reversible. This study reveals an inherent loss in the process, offering a method to calculate and approximate this unavoidable loss.

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Area of Science:

  • Quantum Information Theory
  • Quantum Entanglement

Background:

  • Entanglement concentration for bipartite pure states is widely assumed to be asymptotically reversible.
  • This assumption is crucial for many quantum information processing protocols.

Purpose of the Study:

  • To precisely formulate the problem of entanglement concentration reversibility.
  • To investigate the trade-off between performance and reversibility in entanglement concentration.
  • To quantify the unavoidable loss associated with irreversible entanglement concentration.

Main Methods:

  • Developed a precise theoretical formulation of entanglement concentration.
  • Established a trade-off relation between performance and reversibility.
  • Treated entanglement concentration as a form of entangled state compression.
  • Performed numerical calculations to determine the loss.
  • Derived an analytical approximation for the loss.

Main Results:

  • Demonstrated a trade-off relation implying the irreversibility of entanglement concentration.
  • Showed that complete recovery of the initial state is impossible due to inherent loss.
  • Quantified this loss through numerical computation.
  • Developed a highly accurate analytical approximation for the loss.

Conclusions:

  • Entanglement concentration is fundamentally irreversible, contrary to prior belief.
  • An unavoidable loss occurs during entanglement concentration, necessitating its quantification.
  • The derived analytical approximation provides a valuable tool for understanding and managing this loss in quantum information theory.