Deterministic transformations of coherent states under incoherent operations

TL;DR

This paper introduces two explicit protocols for deterministic transformations of coherent states and pure bipartite entangled states under incoherent operations, expanding the understanding of state transformations in quantum information.

Contribution

It presents permutation-based and sequential protocols for transforming coherent states, including generalized solutions for specific cases, advancing the practical methods for quantum state manipulation.

Findings

Protocols enable single-step and sequential transformations of d-dimensional coherent states.

Solutions extend to deterministic transformations of pure bipartite entangled states.

The methods are based on majorization conditions and permutation strategies.

Abstract

It is well known that the majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this paper, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single-step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where we use $d'$-level ($d'$ $<$ $d$) subspace solutions of the permutation-based protocol to achieve the complete transformation as a sequence of coherent-state transformations. We show that these two protocols also provide solutions for deterministic transformations of pure bipartite entangled states.