Deterministic transformations of bipartite pure states

TL;DR

This paper presents explicit protocols for deterministic transformations of bipartite pure states across various dimensions, including solutions for 3x3 states and a general method for n x n states using specific measurements.

Contribution

It introduces new explicit protocols for deterministic state transformations in bipartite systems, extending to higher dimensions with practical measurement strategies.

Findings

Explicit solutions for 3x3 state transformations.

A general protocol for n x n state transformations.

Demonstrates the feasibility of deterministic transformations with specific measurements.

Abstract

We propose an explicit protocol for the deterministic transformations of bipartite pure states in any dimension using deterministic transformations in lower dimensions. As an example, explicit solutions for the deterministic transformations of $3\otimes 3$ pure states by a single measurement are obtained, and an explicit protocol for the deterministic transformations of $n\otimes n$ pure states by three-outcome measurements is presented.