Explicit C*-algebraic Protocol for Exact Universal Embezzlement of Entanglement

TL;DR

This paper introduces an explicit, exact, and state-independent C*-algebraic protocol for universal entanglement embezzlement, advancing the theoretical understanding of quantum entanglement manipulation in infinite-dimensional systems.

Contribution

It provides the first explicit, exact, and universal embezzlement protocol in the C*-algebraic model, extending previous approximate methods to exact and state-independent cases.

Findings

Achieves exact embezzlement of bipartite pure states with a fixed catalyst

Recovers the Type III_1 factor in the dense-state case via GNS construction

Extends to all states using a non-separable C*-algebra

Abstract

We present an explicit construction of a universal embezzlement protocol in the C*-algebraic model of quantum information, that is equivalent to the commuting operator model. Our protocol enables exact embezzlement of arbitrary bipartite pure states using a single, fixed catalyst state. Unlike prior constructions that achieve only approximate embezzlement or require state-dependent catalysts, our approach is both exact and state-independent. The construction is explicit, based on simple *-automorphisms acting locally on infinite tensor products of CAR algebras with the underlying idea of the Hilbert hotel. In the dense-state case, the protocol naturally recovers the Type III_1 factor via the GNS construction, consistent with recent classification results. We further extend the construction to allow exact embezzlement of all states, at the cost of working with a non-separable C*-algebra. Despite the increase in algebraic size, the operational structure remains simple and localized. This offers a conceptually intuitive model for universal entanglement embezzlement in infinite-dimensional settings.