Lindblad evolutions, Born rule, Heralding and cloning

TL;DR

This paper addresses the challenge of calculating radiation from Lindblad-evolving systems by linking it to the Born rule and demonstrates that heralding, a quantum state preparation method, aligns with no-cloning principles despite not being a completely positive map.

Contribution

It introduces a novel perspective on Lindblad evolution calculations using the Born rule for conserved currents and clarifies the consistency of heralding with no-cloning.

Findings

Radiation emission calculation difficulty resolved via conserved currents and the Born rule.

Heralding is shown to be consistent with no-cloning despite not being a completely positive map.

Provides a new framework for understanding quantum state preparation and evolution.

Abstract

We discuss an apparent difficulty in computing the radiation emitted by a system undergoing Lindblad evolution. The difficulty is resolved by viewing the problem as Born rule for conserved currents defined by the appropriate terms in the adjoint Lindbladian. In Heralding Alice prepares Bob's system in a state that mirrors her test. We show that heralding is consistent with no-cloning. This follows from the observation that heralding is not a completely positive map.