Private quantum channels for multi-photon pulses and unitary k-designs

TL;DR

This paper investigates secure quantum communication channels for multi-photon pulses, demonstrating that certain random unitary channels and qubit unitary k-designs can ensure security under specific conditions.

Contribution

It introduces conditions under which multi-photon quantum channels remain secure and analyzes the security implications of qubit unitary k-designs.

Findings

Random SU(2) Haar-distributed channels ensure security for multi-photon pulses.

Qubit unitary k-designs guarantee security if photon parity is guaranteed.

Security is not assured by k-designs without parity constraints.

Abstract

We address the question of existence of private quantum channel for qubits encoded in polarization degrees of freedom of a photon, that remains secure even if multi-photon (instead of single-photon) pulse is emitted. We show that random unitary channel distributed according to SU(2) Haar measure has this property. Further we analyze the qubit unitary k-designs. We show they ensure security if the photons' parity of the source is guaranteed. Otherwise, the qubit unitary k-designs do not guarantee perfect security.