Relativistically covariant state-dependent cloning of photons

TL;DR

This paper investigates how relativistic covariance constraints affect the optimal fidelity of symmetric state-dependent cloning of photons, revealing states with classical cloning fidelity and implications for quantum cryptography security.

Contribution

It introduces a relativistically covariant framework for photon cloning, showing how Lorentz transformations impact cloning fidelity and security in quantum communication.

Findings

Optimal cloning fidelity can drop to classical limit of 2/3 due to relativistic effects

Certain states exhibit fidelity loss under Lorentz covariance constraints

Implications for BB84 protocol security are discussed

Abstract

The influence of the relativistic covariance requirement on the optimality of the symmetric state-dependent 1 -> 2 cloning machine is studied. Namely, given a photonic qubit whose basis is formed from the momentum-helicity eigenstates, the change to the optimal cloning fidelity is calculated taking into account the Lorentz covariance unitarily represented by Wigner's little group. To pinpoint some of the interesting results, we found states for which the optimal fidelity of the cloning process drops to 2/3 which corresponds to the fidelity of the optimal classical cloner. Also, an implication for the security of the BB84 protocol is analyzed.