Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement

Abstract

We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tensor products of Hilbert spaces; and a natural model of quantum information processing for abstract states on C*-algebras, where joint systems are represented by tensor products of C*-algebras. We call this the C*-circuit model and show that it is a special case of the commuting-operator model (in that it can be translated into such a model). For the conventional model, we show that there exists a constant ${\epsilon }_0>0$ such that self-embezzlement cannot be achieved with precision parameter less than ${\epsilon }_0$ (i.e., the fidelity cannot be greater than $1-{\epsilon }_0$); whereas, in the C*-circuit model -- as well as in a commuting-operator model -- the precision can be $0$ (i.e., fidelity~$1$).

References in corpus (8)

• Connes' embedding problem and Tsirelson's problem
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Tsirelson's problem and an embedding theorem for groups arising from non-local games
• Tsirelson's Problem
• Perfect Embezzlement of Entanglement
• Spatial Search on Graphs with Multiple Targets using Flip-flop Quantum Walk
• Non-Markovian quantum interference in multilevel quantum systems: Exact master equation approach
• A three-player coherent state embezzlement game

Cited by in corpus (1)

• Uniqueness of purifications is equivalent to Haag duality