Optimal quantum operations at zero energy cost

TL;DR

This paper investigates how to manipulate quantum coherence without energy exchange, identifying optimal energy-preserving operations and developing recursive protocols to enhance fidelity and success probability in various quantum tasks.

Contribution

It introduces the first comprehensive analysis of energy-preserving quantum operations, including recursive protocols and approximations for optimal fidelity-probability trade-offs.

Findings

Optimal energy-preserving operations for state conversion identified

Recursive filtering protocols improve success probability and fidelity

Applications demonstrated in quantum metrology, cloning, and coherence purification

Abstract

Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserving filters increases the probability of success while reaching maximum fidelity at each iteration. Building on the recursive protocol, we construct efficient approximations of the optimal fidelity-probability trade-off, by taking coherent superpositions of the different branches generated by probabilistic filtering. The benefits of this construction are illustrated in applications to quantum metrology, quantum cloning, coherent state amplification, and ancilla-driven computation. Finally, we extend our results to transitions where the input state is generally mixed and we apply our findings to the task of purifying quantum coherence.