Impossibility of Cloning of Quantum Coherence

TL;DR

This paper proves that quantum coherence cannot be cloned, even when considering ancillary systems, and characterizes the conditions under which coherence cloning might be possible, extending the no-cloning principle.

Contribution

It establishes the impossibility of cloning quantum coherence for arbitrary states and characterizes the specific states where cloning could be feasible.

Findings

Cloning of quantum coherence is impossible for arbitrary states.

The class of states for which coherence cloning is possible is characterized.

Maximum range of states with perfect coherence cloning is identified.

Abstract

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the 'no-cloning of quantum state'. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states.