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The Forbidden Quantum Adder.

U Alvarez-Rodriguez1, M Sanz1, L Lamata1

  • 1Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain.

Scientific Reports
|July 9, 2015
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Summary
This summary is machine-generated.

Quantum computing faces limitations: adding unknown quantum states is impossible due to the no-cloning theorem. However, an approximate quantum adder for known states is proposed for experimental implementation.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing

Background:

  • Quantum information offers distinct computational advantages over classical information.
  • The no-cloning theorem is a fundamental principle in quantum physics, prohibiting the exact copying of an arbitrary unknown quantum state.

Purpose of the Study:

  • To investigate the feasibility of a quantum adder for unknown quantum states.
  • To explore the limitations imposed by quantum physics on quantum information processing.
  • To propose a potential experimental approach for quantum addition.

Main Methods:

  • Proving the impossibility of a unitary protocol for adding unknown quantum states across different Hilbert spaces.
  • Demonstrating the prohibition of a quantum adder for known orthonormal bases without an ancillary system.
  • Developing an approximate quantum adder protocol.

Main Results:

  • It is proven that no unitary protocol can add unknown quantum states from different Hilbert spaces, stemming from the no-cloning theorem.
  • A quantum adder for known orthonormal bases is shown to be forbidden without an ancillary system.
  • An approximate quantum adder is proposed, suitable for laboratory implementation.

Conclusions:

  • The addition of unknown quantum states is an inherent restriction in quantum physics.
  • While a perfect quantum adder for unknown states is impossible, an approximate version for known states is feasible.
  • Distinctions exist between forbidden quantum adders for states and allowed ones for density matrices.