Probabilistically Perfect Cloning of Two Pure States: A Geometric Approach

TL;DR

This paper introduces a geometric approach to optimally clone two known pure quantum states with minimal failure, revealing a connection to state discrimination and a phase transition phenomenon.

Contribution

It provides a novel geometric solution for probabilistic perfect cloning of two pure states with arbitrary priors, unifying cloning and discrimination.

Findings

Optimal cloning success probability derived

Cloning converges to state discrimination as clones increase

Phase transition-like behavior observed in cloning process

Abstract

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation also reveals a deeper connection between cloning and state discrimination. The convergence of cloning to state discrimination as the number of clones goes to infinity exhibits a phenomenon analogous to a second order symmetry breaking phase transition.