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$$\gt$$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 $1$).

Self-embezzlement is not a non-local game, hence our results do not impact the celebrated Connes Embedding conjecture. Instead, the significance of these results is to exhibit a reasonably natural quantum information processing problem for which there is a constant gap between the capabilities of the conventional Hilbert space model and the commuting-operator or C*-circuit model.

中文翻译：

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传统策略与基于 C*-动态自盗的策略之间的持续差距

我们考虑一种称为 $self-embezzlement$ 的二分变换，并用它来证明两个量子信息模型的能力之间的恒定差距：传统模型，其中二分系统由希尔伯特空间的张量积表示；以及 C*-代数上抽象状态的量子信息处理的自然模型，其中联合系统由 C*-代数的张量积表示。我们称其为 $C*-circuit$ 模型，并表明它是通勤运营商模型的一个特例（因为它可以转化为这样的模型）。对于常规模型，我们证明存在一个常数$epsilon_0$$\gt$$0$，使得精度参数小于$\epsilon_0$（即保真度不能大于$1-\ epsilon_0$); 然而，

自盗不是非本地游戏，因此我们的结果不会影响著名的 Connes Embedding 猜想。相反，这些结果的意义在于展示一个合理自然的量子信息处理问题，对于该问题，传统希尔伯特空间模型与通勤算子或 C* 电路模型的能力之间存在恒定差距。