Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum entanglement. Specifically, we construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show: For every $d,\ell\ge k$, there is an efficient channel $\Lambda: \mathbb{C}^{d\ell} \otimes \mathbb{C}^{d\ell} \to \mathbb{C}^{dk}$ such that for every bipartite separable state $\rho_1\otimes \rho_2$, the output $\Lambda(\rho_1\otimes\rho_2)$ is close to a k-partite separable state. Concretely, for some distribution $\mu$ on states from $\mathbb{C}^d$, $$ \left\|\Lambda(\rho_1 \otimes \rho_2) - \int | \psi \rangle \langle \psi |^{\otimes k} d\mu(\psi)\right\|_1 \le \tilde O \left(\left(\frac{k^{3}}{\ell}\right)^{1/4}\right). $$ Moreover, $\Lambda(| \psi \rangle \langle \psi |^{\otimes \ell}\otimes | \psi \rangle \langle \psi |^{\otimes \ell}) = | \psi \rangle \langle \psi |^{\otimes k}$. Without the bipartite unentanglement assumption, the above bound is conjectured to be impossible. Leveraging our disentanglers, we show that unentangled quantum proofs of almost general real amplitudes capture NEXP, greatly relaxing the nonnegative amplitudes assumption in the recent work of QMA^+(2)=NEXP. Specifically, our findings show that to capture NEXP, it suffices to have unentangled proofs of the form $| \psi \rangle = \sqrt{a} | \psi_+ \rangle + \sqrt{1-a} | \psi_- \rangle$ where $| \psi_+ \rangle$ has non-negative amplitudes, $| \psi_- \rangle$ only has negative amplitudes and $| a-(1-a) | \ge 1/poly(n)$ with $a \in [0,1]$. Additionally, we present a protocol achieving an almost largest possible gap before obtaining QMA^R(k)=NEXP$, namely, a 1/poly(n) additive improvement to the gap results in this equality.

翻译：量子纠缠是多种应用中的关键促成要素。然而，非期望的对抗性纠缠也给许多应用带来了挑战。本文探索了"打破"量子纠缠的方法。具体而言，我们从二分非纠缠输入出发，构造了一个维度无关的k部分解缠器（类）通道。我们证明：对于任意$d,\ell\ge k$，存在一个高效通道$\Lambda: \mathbb{C}^{d\ell} \otimes \mathbb{C}^{d\ell} \to \mathbb{C}^{dk}$，使得对于任意的二分可分离态$\rho_1\otimes \rho_2$，输出$\Lambda(\rho_1\otimes\rho_2)$接近于k部分可分离态。具体地，对于$\mathbb{C}^d$上某种状态分布$\mu$，有： $$ \left\|\Lambda(\rho_1 \otimes \rho_2) - \int | \psi \rangle \langle \psi |^{\otimes k} d\mu(\psi)\right\|_1 \le \tilde O \left(\left(\frac{k^{3}}{\ell}\right)^{1/4}\right). $$ 此外，$\Lambda(| \psi \rangle \langle \psi |^{\otimes \ell}\otimes | \psi \rangle \langle \psi |^{\otimes \ell}) = | \psi \rangle \langle \psi |^{\otimes k}$。若没有二分非纠缠假设，上述界被推测不可能实现。利用我们的解缠器，我们证明几乎一般实振幅的非纠缠量子证明能够捕捉NEXP，极大地放宽了近期QMA^+(2)=NEXP工作中非负振幅的假设。具体地，我们的发现表明：要捕捉NEXP，只需具有形式$| \psi \rangle = \sqrt{a} | \psi_+ \rangle + \sqrt{1-a} | \psi_- \rangle$的非纠缠证明，其中$| \psi_+ \rangle$具有非负振幅，$| \psi_- \rangle$仅具有负振幅，且$| a-(1-a) | \ge 1/poly(n)$，$a \in [0,1]$。此外，我们提出一个协议，在达到QMA^R(k)=NEXP之前实现了几乎最大的可能间隙，即对该间隙进行1/poly(n)的加性改进即可实现该等式。