Complementarity of Quantum Correlations in Cloning and Deleting of Quantum State

TL;DR

This paper investigates the relationship between quantum correlations generated during imperfect cloning and deletion of quantum states, revealing a complementary trade-off affecting the fidelity of these processes.

Contribution

It introduces a bound on total correlations in cloning and deleting, highlighting a new complementarity between quantum correlations needed for copying and restoring states.

Findings

Derived a bound on total correlations in cloning and deleting

Identified a trade-off between cloning fidelity and deletion difficulty

Showed that better cloning increases the challenge of state restoration

Abstract

We quantify the amount of correlation generated between two different output modes in the process of im- perfect cloning and deletion processes. We use three different measures of correlations and study their role in determining the fidelity of the cloning and deletion. We obtain a bound on the total correlation generated in the successive process of cloning and deleting operations. This displays a new kind of complementary relationship between the quantum correlation required in generating a copy of a quantum state and the amount of correlation required in bringing it back to the original state by deleting and vice versa. Our result shows that better we clone (delete) a state, more difficult it will be to bring the state back to its original form by the process of deleting (cloning).