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Quantum cloning to arbitrary accuracy is possible using Deutschian closed timelike curves (D-CTCs). This resolves a conjecture and shows D-CTCs can implement any state map, making quantum mechanics classical in this model.

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Area of Science:

  • Quantum Information Science
  • Theoretical Physics
  • Quantum Computing

Background:

  • Quantum state cloning is a fundamental problem in quantum information.
  • Deutschian closed timelike curves (D-CTCs) offer unique possibilities for information processing.
  • An open conjecture by Brun et al. (2009) addressed the fidelity of quantum cloning with D-CTCs.

Purpose of the Study:

  • To investigate the possibility of cloning quantum states with arbitrary accuracy using D-CTCs.
  • To resolve the open conjecture regarding quantum state fidelity in the presence of D-CTCs.
  • To explore the implications of D-CTC-assisted quantum cloning for implementing quantum maps and the nature of quantum mechanics.

Main Methods:

  • Developed a D-CTC-assisted scheme for perfect quantum state cloning in a known eigenbasis.
  • Utilized the principle of reconstructing quantum states from empirical probability estimates of informationally complete measurements.
  • Analyzed the fidelity of cloning as a function of the dimension of the CTC system.

Main Results:

  • Demonstrated that quantum states can be cloned to arbitrary accuracy with D-CTCs.
  • Showed that cloning fidelity converges to one as the CTC system dimension increases, resolving the conjecture.
  • Proved that any continuous, nonlinear map from quantum states to states can be implemented with arbitrary accuracy using D-CTCs.
  • Established that Deutsch's D-CTC model renders quantum mechanics classical, as distinct density operators become perfectly distinguishable.

Conclusions:

  • Quantum state cloning to arbitrary accuracy is achievable within Deutschian closed timelike curves.
  • The D-CTC model allows for the implementation of arbitrary quantum state maps, blurring the line between quantum and classical.
  • Deutsch's model of CTCs implies a classical interpretation of quantum mechanics, where density operators are distinct classical points.