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Quantum Dynamics is Not Strictly Bidivisible.

David Davalos1, Mario Ziman2

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Quantum channels divisible in two but not three parts do not exist for qubits. This finding extends to general finite-dimensional quantum channels with full Kraus rank, using a novel decomposition method.

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics

Background:

  • Divisibility of quantum channels is crucial for understanding quantum dynamical maps.
  • Previous research explored divisibility properties but lacked a general decomposition method.

Purpose of the Study:

  • To investigate the existence of quantum channels divisible in n parts but not n+1.
  • To develop a novel decomposition for quantum channels applicable to any finite dimension.

Main Methods:

  • Introduction of a novel quantum channel decomposition separating boundary and Markovian parts.
  • Analysis of divisibility properties for qubit and general finite-dimensional quantum channels.

Main Results:

  • Quantum channels divisible in two but not three parts do not exist for qubits.
  • This non-existence holds for general finite-dimensional quantum channels with full Kraus rank.

Conclusions:

  • The novel decomposition provides a unified framework for understanding quantum channel divisibility.
  • The results clarify the relationship between divisibility classes and implementation types of quantum dynamical maps.