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Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.

V Yerokhin¹, A Shehu¹, E Feldman²

¹Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.

Physical Review Letters

|June 4, 2016

Summary

This summary is machine-generated.

This study solves the problem of creating perfect quantum clones from known states with minimal error. The solution uses a geometric approach, revealing a phase transition in the cloning process.

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Area of Science:

Quantum information science
Quantum mechanics
Information theory

Background:

The quantum cloning problem is a fundamental challenge in quantum information.
Previous solutions were limited to specific cases or assumptions.
Arbitrary a priori probabilities for known states complicate the cloning process.

Purpose of the Study:

To solve the problem of creating n perfect quantum clones from m copies of one of two known pure states.
To minimize failure probability in the general case with arbitrary a priori probabilities.
To provide a new theoretical framework for quantum cloning.

Main Methods:

A novel geometric formulation of the quantum cloning problem.
Analysis of the convergence of cloning to state discrimination and preparation.
Investigation of symmetry-breaking phenomena in the cloning process.

Main Results:

A general solution for the n-clone from m-copy problem with minimum failure probability.
Demonstration that cloning converges to state discrimination and preparation as n approaches infinity.
Identification of a second-order symmetry-breaking phase transition analogous to physical systems.

Conclusions:

The geometric formulation provides a powerful tool for understanding quantum cloning.
The identified phase transition offers new insights into the fundamental limits of quantum information processing.
This work advances the theoretical understanding of quantum state replication.