Deciding separability with a fixed error

Towards efficient algorithm deciding separability of distributed quantum states

It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly exponentially with the state's rank. Nevertheless, we argue that for generic states, analysis of concurrence matrices essentially reduces the task of solving separability problem in $m \times n$ dimensions to solving a set of linear equations in about $\binom{mn+D-1}{D}$ variables, where $D$ decreases with $mn$ and for large $mn$ it should not exceed 4. Moreover, the s…

Deciding whether a quantum state has secret correlations is an NP-complete problem

From the NP-hardness of the quantum separability problem and the relation between bipartite entanglement and the secret key correlations, it is shown that the problem deciding whether a given quantum state has secret correlations in it or not is in NP-complete.

On the generation of random ensembles of qubits and qutrits Computing separability probabilities for fixed rank states

The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.

On deciding whether a Boolean function is constant or not

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.

马德隆流体动力学中的局域复依赖与可分性

Local Complex Dependence and Separability in Madelung Hydrodynamics

该研究针对多粒子纯态，提出马德隆流体动力学中局域可分性与依赖的诊断方法，通过波函数对数的混合导数分析，揭示交叉块与可分性的关联，可用于相关量子态性质的判定。

作为量子信道的 Wilsonian 重整化与不动点处的可分性

Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points

将 Wilsonian 重整化表述为量子信道作用于动量空间密度矩阵，证明不动点处理论真空在动量尺度间无纠缠，结果源于尺度对称性并约束基态与期望值。